Geodesic
A~General Approach to the Theory of Nonexistence of Global Solutions to Nonlinear Partial Differential Equations and Inequalities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 285-297.

Voir la notice de l'article provenant de la source Math-Net.Ru

A number of statements on the nonexistence of solutions to differential inequalities are proved with the use of the concept (introduced by the author) of nonlinear capacity induced by a differential operator. The results obtained jointly with E. Mitidieri, A. Tesei, and L. Veron are presented. 
@article{TM_2002_236_a28,
     author = {S. I. Pokhozhaev},
     title = {A~General {Approach} to the {Theory} of {Nonexistence} of {Global} {Solutions} to {Nonlinear} {Partial} {Differential} {Equations} and {Inequalities}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {285--297},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a28/}
}
TY  - JOUR
AU  - S. I. Pokhozhaev
TI  - A~General Approach to the Theory of Nonexistence of Global Solutions to Nonlinear Partial Differential Equations and Inequalities
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2002
SP  - 285
EP  - 297
VL  - 236
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2002_236_a28/
LA  - ru
ID  - TM_2002_236_a28
ER  - 
%0 Journal Article
%A S. I. Pokhozhaev
%T A~General Approach to the Theory of Nonexistence of Global Solutions to Nonlinear Partial Differential Equations and Inequalities
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2002
%P 285-297
%V 236
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2002_236_a28/
%G ru
%F TM_2002_236_a28
S. I. Pokhozhaev. A~General Approach to the Theory of Nonexistence of Global Solutions to Nonlinear Partial Differential Equations and Inequalities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 285-297. http://geodesic.mathdoc.fr/item/TM_2002_236_a28/

[1] Pokhozhaev S. I., “O sobstvennykh funktsiyakh uravneniya $\Delta u+\lambda f(u)=0$”, DAN SSSR, 165:1 (1965), 36–39 | Zbl

[2] Pokhozhaev S. I., “Suschestvenno nelineinye emkosti, indutsirovannye differentsialnymi operatorami”, Dokl. RAN, 357:5 (1997), 592–594 | MR | Zbl

[3] Gidas B., Spruck J., “Global and local behavior of positive solutions of nonlinear elliptic equations”, Commun. Pure and Appl. Math., 34 (1981), 525–598 | DOI | MR | Zbl

[4] Mitidieri E., Pokhozhaev S. I., “Otsutstvie globalnykh polozhitelnykh reshenii dlya kvazilineinykh ellipticheskikh neravenstv”, Dokl. RAN, 359:4 (1998), 456–460 | MR | Zbl

[5] Mitidieri E., Pokhozhaev S. I., “Otsutstvie polozhitelnykh reshenii dlya kvazilineinykh ellipticheskikh zadach v $\mathbb{R}^N$”, Tr. MIAN, 227, 1999, 192–222 | MR | Zbl

[6] Ni W.-M., Serrin J., “Non-existence theorems for quasilinear partial differential equations”, Rend. Circ. Mat. Palermo. Ser. 2, Suppl., 8 (1985), 171–185 | MR

[7] Ni W.-M., Serrin J., “Existence and nonexistence theorems for ground states of quasilinear partial differential equations. The anomalous case”, Atti Convegni Lincei, 77 (1986), 231–257

[8] Mitidieri E., Sweers G., van der Vorst R., “Nonexistence theorems for systems of quasilinear partial differential equations”, Diff. Integr. Equat., 8 (1995), 1331–1354 | MR | Zbl

[9] Pokhozhaev S. I., Tesei A., “O kriticheskikh pokazatelyakh otsutstviya reshenii dlya sistem kvazilineinykh parabolicheskikh neravenstv”, Dif. uravneniya, 2001 (to appear)

[10] Levine H. A., “The role of critical exponents in blowup problems”, SIAM Rev., 32 (1990), 262–288 | DOI | MR | Zbl

[11] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | MR

[12] Pohozaev S. I., Tesei A., “Blow-up of nonnegative solutions to quasilinear parabolic inequalities”, Atti Accad. Naz. Lincei. Cl. Sci. Fis. Mat. Natur. Rend. Ser. 9, 11 (2000), 99–109 | MR | Zbl

[13] Escobedo M., Herrero M. A., “Boundedness and blow up for a semilinear reaction-diffusion system”, J. Diff. Equat., 89 (1991), 176–202 | DOI | MR | Zbl

[14] Escobedo M., Levine H. A., “Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations”, Arch. Ration. Mech. and Anal., 129 (1995), 47–100 | DOI | MR | Zbl

[15] Levine H. A., “A Fujita type global existence–global nonexistence theorem for a weakly coupled system of reaction-diffusion equations”, Ztschr. angew. Math. und Phys., 42 (1991), 408–430 | DOI | MR | Zbl

[16] Veron L., Pohozaev S. I., “Blow-up results for nonlinear hyperbolic inequalities”, Ann. Scuola Norm. Super. Pisa. Cl. Sci. Ser. 4, 29:2 (2000), 393–420 | MR | Zbl