Name: Stanislav Ivanovich Pohozaev (Pokhozhaev)

Prof. Stanislav Pohozaev
Steklov Institute of Mathematics
Gubkina str. 8
Moscow, 119991 Russia

phone: +7-495-9383777 (office)
fax: +7-499-1350555

e-mail:
www: http://www.mi.ras.ru/~pokhozhaev

• Corresponding Member of the Russian Academy of Sciences (since 1984)

• 1986 - present: Principal Researcher at the Steklov Mathematical Institute
• 1971 - 1986: Full Professor, Moscow Power Institute
• 1971 - 1986: Head of the Mathematical Department, Moscow Power Institute
• 1963 - 1971: Associate Professor, Moscow Power Institute
• 1961 - 1963: Research scientist, Institute of Hydrodynamics USSR Acad. Sci.
• 1958 - 1961: Instructor-Assistant, Novosibirsk University

• Nonlinear Functional Analysis
• Nonlinear Variatioanal Problems
• Nonlinear Partial Differential Equations

• Normal solvability of nonlinear equations and Nonlinear Fredholm Alternative
• Nonlinear variational identities (Pokhozhaev identities)
• Embeddings of nonlinear operators and general theory of a priori estimates for solutions of weakly nonlinear equations
• Global fibering method in nonlinear variational problems
• Nonlinear elliptic, parabolic and hyperbolic capacity and its application to the global solvability of nonlinear problems
• Fundamentally new results in the global solvability theory for a wide class of nonlinear problems, including elliptic, parabolic and nonlinear multidimensional hyperbolic problems
• ``Mendeleev's table'' of nonlinear equations and systems for which blow-up criteria have been found. This laid the foundations of a general blow-up theory for global solutions of nonlinear problems. In particular, the dependence of critical exponents on force terms (right-hand side) and initial conditions was established for the first time
• Blow-up of smooth solutions of the KdV equation (with infinite energy)
• Existence of local and global smooth solutions to the (3D) Navier-Stokes equations

• International Conference on Differential Equations and Dynamical Systems, Suzdal (Vladimir region), Russia, June 29–July 04, 2012
• Conference ``Differential Equations and Optimal Control'' dedicated to the 90th anniversary of E.F. Mishchenko, Steklov Mathematical Institute, Moscow, Russia, April 16–17, 2012

• Sixth International Conference on Differential and Functional Differential Equations (DFDE–2011), Moscow, Russia, August 14–21, 2011, talk: ``Blow-up solutions to the Korteweg–de Vries equation.''
• International conference ``Differential Equations and Related Topics'' dedicated to I.G. Petrovskii, Moscow, Russia, May 29–June 4, 2011, talk: ``On singular solutions of the Korteweg–de Vries equation.''

• International Conference ``Nonlinear PDE and Boundary Value Problems with Measure Data,'' Technion – Israel Institute of Technology, Haifa, Israel, March 1–5, 2010, talk: ``Critical nonlinearities in partial differential equations.''

• Second International Conference ``Mathematical Modeling and Differential Equations,'' talk: ``Critical nonlinearities of evolution PDEs,'' Minsk (Belarus), August 24-28, 2009.
• International Conference at the University of Trieste (Italy), talk: ``General theory of eigenfunctions of nonlinear elliptic problems,'' May 21, 2009.
• Leonardo da Vinci Lecture, University of Milan, ``The critical noinlinearities in PDEs,'' May 12, 2009.
• International Conference ``Trends in Nonlinear PDEs,'' talk: ``Embedding of Sobolev spaces in the limit cases and its applications,'' University of Trieste (Italy), May 7, 2009.
• International Conference ``Modern Problems of Mathematics, Mechanics and Their Applications,'' talk: ``Blow-up for PDEs with nonlocal nonlinearities,'' Moscow State University, March 30-April 02, 2009.
• Steklov Mathematical Institute Seminar, ``Blow-up Theory for Nonlinear Partial Differential Equations. Critical Nonlinearities,'' February 26, 2009.

• International Conference ``Mathematical Modelling and Nonlinear Dynamical Systems in Natural Sciences'' dedicated to the 80th birthday of S.P. Kurdyumov, Moscow, November 17-21, 2008.
• The Fifth International Conference on Differential and Functional Differential Equations, Moscow, August 17-24, 2008.
• Liouville Theorems and Detours, Cortona (Italy), May 18-24, 2008.
• International Conference ``Function Spaces, Differential Operators, and General Topology. Problems of Mathematical Education'' dedicated to the 85th birthday of L.D. Kudryavtsev, Moscow, March 25-28, 2008.

• International Conference on Mathematical Modelling and Differential Equations, Minsk, Belarusian State Univ., October 1-5, 2007.
• University of Trieste (Italy), June 25-29, 2007.
• University of Bologna (Italy), June 19-22, 2007.
• University of Padua (Italy), June 11-15, 2007.

1. On a question on supersonic flow. Trudy MPTI. (1958), 1, 167-172
2. On the Dirichlet problem for the equation $\Delta u=u^2$. Doklady Acad Sci. USSR, 136, (1960), no. 3, 769-772
3. The analog of the Schmidt method for a nonlinear equation. Doklady Acad. Sci. USSR 136, (1960), 546-548
4. On the boundary value problem for the equation $\Delta u=u^2$. Doklady Akademii Nauk SU, 138, (1961), no. 2, 305-308
5. The setting of the problem on the strong explosion on the fluid surface, (with A.A.Deribas). Doklady Acad. Sci. USSR. 144, (1962) 3, 524-526
6. On the Sobolev imbedding theorem for $pl=n$. Doclady Conference, Section Math., Moscow Power Inst. (1965), 158-170
7. On eigenfunctions of $\Delta u+\lambda f(u)=0$, Doklady Acad. Sci. SU, 165, (1965), 1, 36-39
8. On a class of operators and solvability of elliptic equations (with Yu.A. Dubinski). Matemat. Sbornik. 72, (1967), N 2, 226-236
9. On the solvability of nonlinear equations with odd operators. Funct. Analysis and Prilozheniya, 1 (1967), N 3, 66-73
10. On eigenfunctions of some nonlinear problems. Doklady Sci.-Tech. Conference MPI, Section Math. (1967), 186-191.
11. On a set of critical values for the functionals. Matemat. Sbornik. 75, (1968) N 1, 106-111
12. On normal solvability of nonlinear equations. Doklady Acad. Sci. USSR. 184, (1968) N 1, С. 40-43
13. On nonlinear operators possessing weakly closed range and quasilinear elliptic equations. Matemat. Sbornik. 78, (1968), N 2, 237-259
14. Normal solvability of nonlinear equations in uniformly convex Banach spaces, Funct. Analysis and Prilozheniya, 3, (1969), N 2, 90-94
15. On a set of the functional level. Doklady Sci.-Tech. Conference MPI, Section Math. (1968), 63-68.
16. Conservation laws and a priori estimates for some parabolic equations. Differentsialnyje Uravnenija. 6, (1970) N 1, 129-136
17. On eigenfunctions of quasilinear elliptic problems, Matemat. Sbornik, 82, (1970), N 2, 192-212
18. On weakly nonlinear hyperbolic systems. Trudy Moscow Math. Society. 23, (1970), 161-76
19. On solvability of quasilinear hyperbolic systems. Doklady Acad. Sci. USSR. 192, (1970), N 6, 1217 - 1220
20. On a quasilinear parabolic equation. Differentsialnyje Uravnenija. 7, (1971), N 1, 73-80
21. On periodic solutions of some nonlinear hyperbolic equations. Doklady Acad. Sci. USSR. 198, (1971), N 6, 1274-1277
22. On some noncoercive quasilinear elliptic problems. Trudy MPI, Mathematics. Iss 89, (1971), 11-19
23. Quasilinear hyperbolic Kirchhoff equations. Trudy MPI, Researshes on Differential Equations and Appl. Iss. 201, (1974)
24. On a class of quasilinear hyperbolic equations. Matemat. Sbornik, 138 (1975), N 1, 152-166
25. Studies of hyperbolic systems of quasilinear equations by the continuation method. Trudy MPI. Iss. 260, (1975), 74-88
26. Questions of nonexistence of solutions for nonlinear boundary problems. Trudy of SU Conference on partial differential equations. MSU Press. (1978) 200-203
27. On an equation for nonisotropic gas flow. Trudy MPI, Appl. Problems of Math., Iss. 357, (1978), 81-87
28. On equations of the form $\Delta u=f(x,u)$ (Abstract) Uspehi Mat. Nauk. 33, (1978), N 3, 149-149
29. On an approach to nonlinear equations, Doklady Acad. Sci. USSR. 247, (1979), N 6, 1327-1331
30. A comparison theorem and nonexistence of solutions for nonlinear boundary problems. Trudy MPI, Appl. Problems of Math., Iss. 499, (1980), 42-48
31. On periodical solutions of some nonlinear systems of ordinary differential equations. Differentsialnyje Uravnenija, 16, (1980), N 1, 109-116
32. On equations of the form $\Delta u=f(x,u,Du)$. Matemat. Sbornik. 113, (1980), N 2, 324-338
33. On a new programm on mathematics for ingeneers, (with S.M. Nikolskii, L.D.Kudrjavcev, L.A.Kuznecov). Sci.-Meth. Iss. in Mathematics. Iss. 9, (1981) 5-12
34. On regional seminars and conferences for heads of the mathematicals departments, (with L.D.Kudrjavcev, L.A.Kuznecov). Sci.-Meth. Iss. in Mathematics. Iss. 9, (1981) 113-122
35. On quasilinear elliptic equations of higher order. Differentsialnyje Uravnenija. 17, (1981), N 1, 115-128
36. On subordinate operators for nonlinear equations. Doklady Acad. Sci. USSR. 257, (1981), N 6, 282-286
37. Nonlinear partial differential equations. Math. Ensicl. 3, (1982), 950-956
38. On solvability of quasilinear elliptic equations of arbitrary order. Matemat. Sbornik. 117, (1982), N 2, 251-265
39. On the general theory of a priori estimates for solutions of nonlinear equations. Trudy MPI, Appl. Problems of Math., Iss. 566, (1982), 62-69
40. On solvability of quasilinear elliptic equations of higher order. Differentsialnyje Uravnenija. 18, (1982), N 1, 100-109
41. On the general theory of a priori estimates for quasilinear equations. Doklady 7 Soviet-Czech Seminar Math. Phys. Probl. Erevan. (1982), 280-285
42. On an approach to nonlinear equations and its applications. Uspechi Mat. Nauk. 37, (1982), N 2, 261-261
43. On the general theory of a priori estimates for nonlinear equations (Abstract). Uspechi Mat. Nauk. 37, (1982), N 4, 90
44. Embedding of nonlinear operators and a priori estimates for solutions of nonlinear equations. Doklady Acad. Sci. USSR. 266, (1982), N 5, 1063-1066
45. On a priori estimates for solutions of nonlinear equations. Abstracts of USSR Lavrentijev Conference. Novosibirsk. (1982), 24-25
46. On a priori estimates for solutions of quasilinear elliptic equations of arbitrary order. Differentsialnyje Uravnenija. 19, (1983), N 1, 101-110
47. On a fibering method in nonlinear problems. Mezhvedomstvennyi Sbornik po Matemat. MPI. (1985), 5
48. On a quasilinear hyperbolic Kirchhoff equation, Differentsialnyje Uravnenija. 21, (1985), N 1, 101-108
49. On embedding of nonlinear operators and a priori estimates for solutions of nonlinear equations. Partial Differential Equations and Applications. Trudy of USSR symposium (1982), Tbilisi, 203-210
50. On a class of nonlinear noncoercive problems. Researches in nonlinear operators. Ufa. Ural branch of RAS USSR. Bashkirija Sci. Center. Inst. Math. (1988), 5-17
51. On a constructive method of variational calculus, Doklady Acad. Sci. USSR. 298, (1988), N 6, 1330-1333
52. On a Obsjannikov problem. Journal Appl. Mech. Tech. Physics (Russian) (1989), N 2, 5-10
53. Nonlinear Applied Functional Analysis (with V.V. Zharinov, M.A.Illarionov, V.P.Pikulin). MPI Press. (1989)
54. Practical Course in Equations of Mathematical Physics, (with V.P.Pikulin). MPI Press. (1989)
55. On the fibering method of the solvability of the nonlinear boundary problems, Proc. Steklov Math. Inst., 192, (1990), 146-163
56. On solvability of an elliptic problem in $\Bbb R^N$ with supercritical exponent. Doklady Acad. Sci. USSR 313, (1990), N 6, 1356-1360
57. On positivity classes for elliptic operators in $\Bbb R^N$ with supercritical exponent. Doklady Acad. Sci. USSR. 314, (1990), N 3, 558-561
58. On a new interal relation and its application to nonlinear elliptic problems. In: Abstracts. III International Lavrentijev Conference in Math., Mech. and Phys. 10-14 September 1990. (1990) 34
59. On elliptic problems in $R^N$ with supercritical exponent of nonlinearity. Matemat. Sbornik. 182, (1991), N 4, 467-489
60. On entire solutions of quasilinear elliptic equations. Doklady Acad. Sci. USSR. 318, (1991), N 4, 815-820
61. On entire solutions of a class of the quasilinear elliptic equations. Doklady Acad. Sci. USSR. Т. 318. (1991), N 6, 1319-1324
62. On the asymptotic of entire radial solutions of quasilinear elliptic equations. Doklady Acad. Sci. USSR. 320, (1991), N 4, 808-813
63. On entire solutions of semilinear elliptic equations. Progress in Partial Differential Equations: Elliptic and Parabolic Problems. Proceedings of I-st European Conference on Elliptic-Parabolic Problems. Ed. C.Bandle at al. Pitman Research Notes in Mathematics. V. 266. (1992), Longman Scientific Technical New York. P. 56-69.
64. On smoothness of solutions to some superlinear elliptic equations. Doklady Acad. Sci. USSR. 327, (1992), N 3, 299-302
65. On sharp a priori estimates for some superlinear elliptic equations. Doklady Acad. Sci. USSR. 327, (1992), N 4-6, 433-437
66. On quasilinear elliptic problems in $\Bbb R^N$ in the supercritical case. Proc. Steklov Math. Inst. 201, (1992), 324-341
67. On entire radial solutions to some nonlinear elliptic equations. Matemat. Sbornik. 183, (1992), N 11, 3-18
68. On a mathematical model of electrolysis. Doklady Acad. Sci. USSR. 332, (1993), N 6, 18-20
69. On entire radial solutions to quasilinear elliptic equations. Proc. Steklov Math. Inst. 204, (1993), 251-273
70. Sharp a priori estimates for a quasilinear degenerate elliptic problem. Matemat. Sbornik. 184, (1993), N 8, 3-16
71. The sharp apriori estimates for some quasilinear elliptic equations. Differentsialnyje Uravnenija. 29, (1993), N 3, 472-486
72. The sharp apriori estimates for some superlinear degenerate elliptic problems. "Function spaces, Differential operators and Nonlinear Analysis", Teubner - Texte zur Mathematik, Bd. 133, (1993), 200-217
73. On a nonlinear problem of electrolysis. Matemat. Sbornik. 185, (1994), N 5, 103-118
74. On a nonlinear elliptic problem of H.Amann. Differentsialnyje Uravnenija. 30, (1994), N 4, 675-690
75. On a quasilinear system of equations of electric-chemical diffusion. Proc. Steklov Math. Inst. 210, (1995), 239-263
76. On the Maslov equations. Differentsialnyje Uravnenija. 31, (1995), N 2, 338-349
77. Practical Course in the Equations of Mathematical Physics, (with V.P.Pikulin). Moscow: Nauka. (1995)
78. Positive solutions for the $p$-Laplacian: application of the fibering method (with P. Drabek) Proc. of Roy. Soc. Edinburgh, v.127A (1997), N 3, 703-726
79. The fibering method in nonlinear variational problems, Russian Mathematical Surveys, v.51, N 5 (1996), 204
80. The fibering method in nonlinear variational problems, Pitman Research Notes in Mathematics, v. 365 (1997), 35-88
81. On the Reaction-Diffusion-Electrolysis nonliner elliptic equations, Lectures Notes in Pure and Applied Mathematics Series, v.194 (1997), 255-288
82. Entire Solutions of Semilinear Elliptic Equations (with I. Kuzin), 1997, Birkhauser, 245 pp.
83. Essential nonlinear capacities induced by differential operators, Doklady Russ.Acad.Sci., v.357, N5 (1997), 592-594.
84. On the global fibering method in nonlinear variational problems, Proc. Steklov Inst. Math., v.219 (1997), 286-334.
85. Nonexistence of global positive solutions to quasilinear elliptic inequalities (with E. Mitidieri), Doklady Russ.Acad.Sci., v.359, N4 (1998), 456-460.
86. On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain (with V. Mustonen), Differential and Integral Equations, v.11, N1 (1998), 133-145.
87. On the existence and nonexistence of periodic solutions for some quasilinear hyperbolic equations, Doklady Russ.Acad.Sci., v.363, N3 (1998), 304-307.
88. Existence of positive solution for some Nonlinear Neumann problems (with A. Tesei), Doklady Russ.Acad.Sci., v.363, N4 (1998), 450-453.
89. The Cauchy problem for the Extended Fisher-Kolmogorov (EFK) equation, (with L.A. Peletier), Differentsialnyie Uravnenija (Russian), v.35, N3 (1999), 351-366.
90. Nonexistence of positive solutions for quasilinear elliptic problems on $\Bbb R^N$ (with E. Mitidieri), Proc. Steklov Inst. Math., v.227 (1999), 192-222.
91. Existence and Nonexistence of periodic solutions to some Nonlinear Hyperbolic Equations, Proc. Steklov Inst. Math., v.227 (1999), 260-285.
92. The Fibering method and its Applications to Nonlinear Boundary value problems, Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 1999. Rend. Inst. Math. Univ. Trieste, v. XXXI, 235-305 (1999)
93. Nonexistence of positive solutions for a system of quasilinear elliptic equations and inequalities in $\Bbb R^N$ (with E. Mitidieri), Doklady Russ.Acad.Sci. v.366, N1 (1999), 13-17.
94. On a class of Nonlinear Dirichlet Problems with First Order Terms, Nota Scientifica, 99/33, Dip.Mat. "G.Castelnuovo", Universite' di Roma "La Sapienza" (1999)
95. Existence and Nonexistence of Solutions of Nonlinear Neumann Problems (with A.Tesei), SIAM Journal of Math. Analysis, v. 31 (1999), 119-133.
96. On the Necessary Conditions of Global Existence of Solutions to a Quasilinear Inequality in the Half-space (with Yu.Egorov, V.Galaktionov, and V.Kondratiev), C. R. Acad. Sci. Paris, t. 330, Ser. 1 (2000), 93-98
97. Multiple Positive Solutions of Some Quasilinear Newmann Problems (with L.Veron), Applicable Analysis, v. 74 (3-4), 363-391 (2000)
98. On Conditions of the Existence of Solutions to a Quasilinear Inequality in the Half-space (with V. Galaktionov, Yu. Egorov, and V. Kondratiev), Matemat. Zametki, v. 67, no. 1 (2000), 150-152
99. Nonexistence results of solutions of semilinear differential inequalities on the Heisenberg group (with L. Veron), Manuscripta Math. 102 (2000), 85-99
100. Blow-up of nonnegative solutions to quasilinear parabolic inequalities (with A. Tesei), Rend. Mat. Acc. Lincei, s.9, v.11 (2000), 99-109
101. Existence and Nonexistence of Solutions of Nonlinear Dirichlet Problems with First Order Terms (with Luisa Moschini, A.Tesei), Journal of Functional Analysis 177 (2000), 365-382.
102. Blow-up results for nonlinear hyperbolic inequalities (with L. Veron), Ann. Scuola Norm. Sup. Pisa, C1. Sci. (4), v. 29 (2000), pp. 393-420
103. Nonexistence Results and Estimates for Some Nonlinear Elliptic Problems (with M.F. Bidaut-Veron), Journal d'Analyse Mathematique, vol. 84 (2001), 1-49.
104. Nonexistence of Weak Solutions for Some Degenerate Elliptic and Parabolic Problems on $\Bbb R^N$ (with E. Mitidieri), J. Evolution Equations, vol. 2 (2001), 189-220.
105. Nonexistence of weak solutions for some degenerate and singular hyperbolic problems on $\Bbb R_+^{N+1}$ (with E.Mitidieri), Proc. Steklov Inst. Math., v.232 (2001), 248-267.
106. A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities (with E. Mitidieri), Proc. Steklov Inst. Math., v. 234 (2001), pp. 1-383.
107. Equations in mathematical physics: A practical course (with V.P. Pikulin), Basel: Birkhauser, 2001.
108. On the critical exponent for nonexistence of solutions to the systems of quasilinear parabolic inequalities (with A. Tesei), Diff. Equat., v. 37, no. 4 (2001), pp. 521-528.
109. On a Class of Nonlinear Dirichlet Problems with First Order Terms (with L. Moschini and A. Tesei), Funct. Diff. Equat., v. 8, no.3-4 (2001), pp. 345-352.
110. General approach to the theory of nonexistence of global solutions to nonlinear PDE's and inequalities, Proc. Steklov Inst. Math., v. 236 (2002), pp. 285-297.
111. Instantaneous Blow-up of Solutions to a Class of Hyperbolic Inequalities (with A. Tesei), Proc. Conf. ``Quasilinear Elliptic and Parabolic Equations and Systems" (Luminy, Sept. 3-7, 2001), Electronic Journal of Differential Equations, Conference 08.2002, pp. 155-165.
112. On the nonexistence of solutions to elliptic systems with dynamical boundary conditions (with M. Kirane, E. Nabana), Dif. Eq. (Russian), v. 38, no. 6 (2002), pp. 768-774.
113. Some generalizations of the Bernstein theorem (with E. Mitidieri), Dif. Eq. (Russian), v. 38, no. 3 (2002), pp. 373-378.
114. The Fujita type theorems for quasilinear parabolic inequalities with nonlinear gradient (with E. Mitidieri), Dokl. Akad. Nauk, v. 386, no. 2 (2002), pp. 160-164.
115. On the asymptotics of global solutions of higher-order semilinear parabolic equations in the supercritical range (with Yu.V. Egorov, V.A. Galaktionov, V.A. Kondratiev), C. R. Acad. Sci. Paris, Ser. 1, v. 335 (2002), pp. 805-810.
116. On systems of quasilinear singular parabolic equations and inequalities (with E. Mitidieri), Proc. Petrovskii Seminars, v. 22 (2002), pp. 232-260.
117. Existence and blow-up for higher-order semilinear parabolic equations: Majorizing order-preserving operators (with V.A. Galaktionov), Indiana Univ. Math. J., v. 51, no. 6 (2002), pp. 1321-1338.
118. The General Blow-up Theory for Nonlinear PDE's, in ``Function Spaces, Differential Operators and Nonlinear Analysis: The Hans Triebel Anniversary Volume", Basel: Birkhauser, 2003, pp. 141-159.
119. On the multidimensional scalar conservation laws, Mat. Sbornik, v. 194, no. 1 (2003), pp. 147-160.
120. Blow-up and critical exponents for nonlinear hyperbolic equations. I (with V. Galaktionov), Nonlinear Anal. TMA, v. 53 (2003), pp. 453-466.
121. On the a priori estimates and gradient catastrophes of smooth solutions to hyperbolic systems of conservation laws, Proc. Steklov Inst. Math., vol. 243 (2003), pp. 257-288 [Engl. transl.: 247-277].
122. Positivity property of solutions of some nonlinear elliptic inequalities on $\Bbb R^n$ (with E. Mitidieri), Dokl. Akad. Nauk, v. 393, no. 2 (2003), pp. 159-164 [Engl. transl.: v. 68, no. 3 (2003), pp. 339-344].
123. On the hyperbolic systems of conservation laws, Dif. Eq. (Russian), vol. 39, no. 5 (2003), pp. 663-673.
124. On similarity solutions and blow-up spectra for a semilinear wave equation (with V.A. Galaktionov), Quart. Appl. Math, vol. 61, no. 3 (2003), pp. 583-600.
125. Nonexistence of local solutions to semilinear partial differential inequalities (with A. Tesei), Ann. Inst. Poincare, vol. 21, no. 4 (2004), pp. 487-502.
126. Towards a unified approach to nonexistence of solutions for a class of differential inequalities (with E. Mitidieri), Milan J. Math., vol. 72 (2004), pp. 129-162.
127. On some integral inequalities associated with Riesz potentials (with E. Mitidieri), Dokl. Akad Nauk, vol. 397, no. 6 (2004), pp. 737-742 [Engl. Transl.: Dokl. Math. vol. 70, no. 1 (2004), pp. 623-627].
128. Liouville-type theorems for certain nonlinear nonlocal problems (with E. Mitidieri), Dokl. Akad Nauk, vol. 399, no. 6 (2004), pp. 732-736 [Engl. Transl.: Dokl. Math. vol. 70, no. 3 (2004), pp. 954-958].
129. A practical course in equations of mathematical physics (with V.P. Pikulin), Moscow: Moscow Center for Continuous Math. Education, 2004 (in Russian).
130. Global solutions of higher-order semilinear parabolic equations in the supercritical range (with Yu.V. Egorov, V.A. Galaktionov, and V.A. Kondratiev), Adv. Diff. Eq., vol. 9 (2004), pp. 1009-1038.
131. Nonexistence of global solutions to an elliptic equation with a dynamical boundary condition (with M. Kirane and E. Nabana), Bol. Soc. Parana. Mat. (3), vol. 22, no. 2 (2004), pp. 9-16.
132. Liouville theorems for some classes of nonlinear nonlocal problems (with E. Mitidieri), Proc. Steklov Inst. Math., vol. 248 (2005), pp. 158-178.
133. Representation formulae and inequalities for solutions of a class of second order partial differential equations (with L. D'Ambrosio and E. Mitidieri), Trans. Amer. Math. Soc. vol. 358, no. 2 (2005), pp. 893-910.
134. Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators (with V.A. Galaktionov), J. Evol. Eq., vol. 6, no. 1 (2006), pp. 45-69.
135. Multiple positive solutions to nonlinear Neumann problems via the fibering method, Proc. Int. Workshop "Current Trends in Nonlinear Analysis," Otranto, June 12-16, 2006. To appear.
136. Convergence in gradient systems with branching of equilibria (with V.A. Galaktionov and A.E. Shishkov), Mat. Sbornik, vol. 198, no. 6 (2007), pp. 65-88 [Engl. Transl.: Sb. Math., vol. 198, no. 6 (2007), pp. 817-838]; arXiv:0902.0286v1 [math.AP].
137. On the absence of global solutions of nonlinear mixed problems (with V.A. Galaktionov), Trudy Seminara imeni I.G. Petrovskogo, No. 26 (2007), pp. 71-89 [Engl. Transl.: J. Math. Sci., vol. 143, no. 4 (2007), pp. 3226-3238].
138. Blowup for nonlinear initial-boundary value problems (with V.A. Galaktionov), Dokl. Akad. Nauk, vol. 412, no. 4 (2007), pp. 444-447 [Engl. Transl.: Dokl. Math., vol. 75, no. 1 (2007), pp. 76-79].
139. Nonlinear variational problems via the fibering method, in: Handbook of Differential Equations. Stationary Partial Differential Equations (ed. by M. Chipot), Amsterdam: Elsevier, 2008, vol. 5, pp. 49-209.
140. On the blow-up of solutions to nonlinear initial-boundary value problems, Trudy Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk, vol. 260 (2008), pp. 213-226 [Engl. Transl.: Proc. Steklov Inst. Math., vol. 260 (2008), pp. 204-217].
141. Local estimates and Liouville theorems for a class of quasilinear inequalities (with G. Caristi and E. Mitidieri), Dokl. Akad. Nauk, vol. 418, no. 4 (2008), pp. 453-457 [Engl. transl.: Dokl. Math., vol. 77, no. 1 (2008), pp. 85-89].
142. On blow-up of solutions of the Kuramoto-Sivashinsky equation, Mat. Sb. vol. 199, no. 9 (2008), pp. 97-106 [Engl. transl.: Sb. Math., vol. 199, no. 9 (2008), pp. 1355-1365].
143. Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation (with V.A. Galaktionov and E. Mitidieri), Dokl. Akad. Nauk, vol. 419, no. 4 (2008), pp. 439-442 [Engl. Transl.: Dokl. Math. vol. 77, no. 2 (2008), pp. 238-242].
144. Capacity induced by a nonlinear operator and applications (with V.A. Galaktionov and E. Mitidieri), Georgian Math. J., vol. 15, no. 3 (2008), pp. 501-516.
145. Third-order nonlinear dispersive equations: Shocks, rarefaction, and blowup waves (with V.A. Galaktionov), Zh. Vychisl. Mat. Mat. Fiz., vol. 48, no. 10 (2008), pp. 1819-1846 [Engl. Transl.: J. Comput. Math. Math. Phys., vol. 48, no. 10 (2008), pp. 1784-1810]; arXiv:0902.0253v1 [math.AP].
146. On the nonexistence of global solutions of the Hamilton-Jacobi equation, Diff. Uravn., vol. 44, no. 10 (2008), pp. 1405-1415 [Engl. Transl.: Diff. Eqns., vol. 44, no. 10 (2008), pp. 1467-1477].
147. Variational approach to complicated similarity solutions of higher order nonlinear evolution partial differential equations (with V.A. Galaktionov and E. Mitidieri), in: Sobolev Spaces in Mathematics. II: Applications in Analysis and Partial Differential Equations. New York: Springer, 2009, pp. 147-197 (Int. Math. Ser., vol. 9); arXiv:0902.1425v1 [math.AP].
148. On the blow-up of positive solutions to elliptic equations in plane unbounded domains, Mat. Zametki, vol. 85, no. 2 (2009), pp. 261-272 [Engl. Transl.: Math. Notes, vol. 85, no. 2, pp. 240-250 (2009)].
149. Global solvability of the Kuramoto-Sivashinsky equation with bounded initial data, Mat. Sb., vol. 200, no. 7 (2009), pp. 131-144 [Engl. Transl.: Sb. Math., vol. 200, no. 7, pp. 1075-1088 (2009)].
150. On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations (with V.A. Galaktionov and E. Mitidieri), Nonlinear Anal., Theory Methods Appl., vol. 70, no. 8, 2930-2952 (2009); arXiv:0902.0257v1 [math.AP].
151. Multiple positive solutions of nonlinear boundary value problems, in: Nonlinearity in Modern Natural Science. Moscow: URSS, 2009, pp. 59-69 [in Russian].
152. Some Liouville theorems for quasilinear elliptic inequalities (with G. Caristi and E. Mitidieri), Dokl. Akad. Nauk, vol. 424, no. 6 (2009), pp. 741-747 [Engl. transl.: Dokl. Math., vol. 79, no. 1 (2009), pp. 118-124].
153. Lifespan estimates for solutions of some evolution inequalities (with E. Mitidieri), Diff. Uravn., vol. 45, no. 10 (2009), pp. 1441-1451 [Engl. Transl.: Diff. Eqns., vol. 45, no. 10 (2009), pp. 1473-1484].
154. Critical nonlinearities in partial differential equations, Milan J. Math., vol. 77, no. 1 (2009), pp. 127-150.
155. On the blow-up of sign-changing solutions to semilinear parabolic equations, Dokl. Akad. Nauk, vol. 431, no. 1 (2010), pp. 22-24 [Engl. Transl.: Dokl. Math., vol. 81, no. 2 (2010), pp. 185-187].
156. On a class of singular solutions to the Korteweg-de Vries equation, Dokl. Akad. Nauk, vol. 435, no. 4 (2010), pp. 460-462 [Engl. Transl.: Dokl. Math., vol. 82, no. 3 (2010), pp. 936-938].
157. Concerning an equation in the theory of combustion, Mat. Zametki, vol. 88, no. 1 (2010), pp. 53-62 [Engl. Transl.: Math. Notes, vol. 88 (2010), pp. 48-56].
158. On the singular solutions of the Korteweg-de Vries equation, Mat. Zametki, vol. 88, no. 5 (2010), pp. 770-777 [Engl. Transl.: Math. Notes, vol. 88 (2010), pp. 741-747].
159. On stationary solutions of the Vlasov-Poisson equations, Diff. Uravn., vol. 46, no. 4 (2010), pp. 527-534 [Engl. Transl.: Diff. Eqns., vol. 46, no. 4 (2010), pp. 530-537].
160. Blow-up of sign-changing solutions to quasilinear parabolic equations, Trudy Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk, vol. 269 (2010), pp. 215-224 [Engl. Transl.: Proc. Steklov Inst. Math., vol. 269 (2010), pp. 208-217].
161. On critical nonlinearities in PDEs, in: Mathematics, Informatics, Their Applications and Role in Education: Proc. School-Conf., Moscow, 2009.
162. Blow-up of sign-changing solutions of a quasilinear heat equation, Diff. Uravn., vol. 47, no. 3 (2011), pp. 376-384 [Engl. Transl.: Diff. Eqns., vol. 47, no. 3 (2011), pp. 373-381].
163. On the nonexistence of global solutions of some initial-boundary value problems for the Korteweg-de Vries equation, Diff. Uravn., vol. 47, no. 4 (2011), pp. 493-498 [Engl. Transl.: Diff. Eqns., vol. 47, no. 4 (2011), pp. 488-493].
164. On the dependence of the critical exponent of the nonlinear heat equation on the initial function, Diff. Uravn., vol. 47, no. 7 (2011), pp. 946-953 [Engl. Transl.: Diff. Eqns., vol. 47, no. 7 (2011), pp. 955-962].
165. Weighted identities for solutions of generalized Korteweg-de Vries equations, Mat. Zametki, vol. 89, no. 3 (2011), pp. 393-409 [Engl. Transl.: Math. Notes, vol. 89 (2011), pp. 382-396].
166. Riemann quasi-invariants, Mat. Sb., vol. 202, no. 6 (2011), pp. 111-132 [Engl. Transl.: Sb. Math., vol. 202, no. 6 (2011), pp. 887-907].
167. Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II (with V.A. Galaktionov and E. Mitidieri), Nonlinear Anal., Real World Appl., vol. 12, no. 4 (2011), pp. 2435-2466; arXiv:1103.2643v1 [math.AP].
168. On the existence and nonexistence of solutions of some quasilinear hyperbolic equations, Diff. Uravn., vol. 47, no. 12 (2011), pp. 1732-1740 [Engl. Transl.: Diff. Eqns., vol. 47, no. 12 (2011), pp. 1754-1762].
169. Nonexistence of global solutions to the KdV equation, Sovrem. Mat., Fundam. Napravl., vol. 39 (2011), pp. 141-150.
170. On a class of initial-boundary value problems for equations of Korteweg-de Vries type, Diff. Uravn., vol. 48, no. 3 (2012), pp. 368-374 [Engl. Transl.: Diff. Eqns., vol. 48, no. 3 (2012), pp. 372-378].
171. Blow-up of smooth solutions of the Korteweg--de Vries equation, Nonlinear Anal., Theory Methods Appl., Ser. A: Theory Methods, vol. 75, no. 12 (2012), pp. 4688-4698.
172. Blow-up of global sign-changing solutions of a nonlinear heat equation, Dokl. Akad. Nauk, vol. 443, no. 3 (2012), pp. 296-299 [Engl. Transl.: Dokl. Math., vol. 85, no. 2 (2012), pp. 225-228].
173. Global Sign-changing Solutions of a Higher Order Semilinear Heat Equation in the Subcritical Fujita Range (with V.A. Galaktionov and E. Mitidieri), Advanced Nonlinear Studies, vol. 12, no. 3 (2012), pp. 569-596.
174. Classification of Global and Blow-up Sign-Changing Solutions of a Semilinear Heat Equation in the Subcritical Fujita range (with V.A. Galaktionov and E. Mitidieri), to appear.