@article{AIHPC_2004__21_4_487_0, author = {Pohozaev, Stanislav I and Tesei, Alberto}, title = {Nonexistence of local solutions to semilinear partial differential inequalities}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {487--502}, publisher = {Elsevier}, volume = {21}, number = {4}, year = {2004}, doi = {10.1016/j.anihpc.2003.06.002}, mrnumber = {2069634}, zbl = {1064.35220}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.002/} }
TY - JOUR AU - Pohozaev, Stanislav I AU - Tesei, Alberto TI - Nonexistence of local solutions to semilinear partial differential inequalities JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 487 EP - 502 VL - 21 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.002/ DO - 10.1016/j.anihpc.2003.06.002 LA - en ID - AIHPC_2004__21_4_487_0 ER -
%0 Journal Article %A Pohozaev, Stanislav I %A Tesei, Alberto %T Nonexistence of local solutions to semilinear partial differential inequalities %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 487-502 %V 21 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.002/ %R 10.1016/j.anihpc.2003.06.002 %G en %F AIHPC_2004__21_4_487_0
Pohozaev, Stanislav I; Tesei, Alberto. Nonexistence of local solutions to semilinear partial differential inequalities. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 4, pp. 487-502. doi : 10.1016/j.anihpc.2003.06.002. http://www.numdam.org/articles/10.1016/j.anihpc.2003.06.002/
[1] Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. 1-B (1998) 223-262. | MR | Zbl
, ,[2] Blow up for ut−Δu=g(u) revisited, Adv. Differential Equations 1 (1996) 73-90. | Zbl
, , , ,[3] Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Compl. Madrid 10 (1997) 443-469. | MR | Zbl
, ,[4] Weak eigenfunctions for the linearization of extremal elliptic problems, J. Funct. Anal. 156 (1998) 30-56. | MR | Zbl
, ,[5] Existence versus explosion instantanée pour des equations de la chaleur linéaires avec potentiel singulier, C. R. Acad. Sci. Paris 329 (1999) 973-978. | MR | Zbl
, ,[6] Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR | Zbl
, , ,[7] Mathematical Analysis and Numerical Methods for Science and Technology, vol. I, Springer, 1985. | Zbl
, ,[8] Some nonexistence results for quasilinear elliptic problems, J. Math. Anal. Appl. 252 (2000) 256-277. | MR | Zbl
,[9] A nonlinear elliptic PDE with the inverse square potential, J. Anal. Math. 86 (2002) 359-398. | MR | Zbl
,[10] Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525-598. | MR | Zbl
, ,[11] Nonlinear PDE with vector fields, J. Anal. Math. 81 (2000) 111-137. | MR | Zbl
,[12] Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal. 49 (1973) 241-269. | MR | Zbl
, ,[13] Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math. 135 (1989) 233-272. | MR | Zbl
, , , ,[14] The absence of global positive solutions to quasilinear elliptic inequalities, Dokl. Russ. Acad. Sci. 359 (1998) 456-460. | MR | Zbl
, ,[15] A Priori Estimates and Blow-Up of Solutions to Nonlinear Partial Differential Equations and Inequalities, Proc. Steklov Inst. Math., vol. 234, International Academic Publishing, Moscow, 2001. | MR | Zbl
, ,[16] Existence and nonexistence of solutions of nonlinear Dirichlet problems, J. Funct. Anal. 177 (2000) 365-382. | MR | Zbl
, , ,[17] On a class of nonlinear Dirichlet problems with first order terms, in: International Conference on Differential and Functional Differential Equations, Moscow, 1999, Funct. Differ. Equations 8 (2001) 345-352. | MR | Zbl
, , ,[18] Blow-up of nonnegative solutions to quasilinear parabolic inequalities, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 11 (2000) 99-109. | MR | Zbl
, ,[19] Instantaneous blow-up of solutions to a class of hyperbolic inequalities, Electronic J. Differential Equations Conference 08 (2002) 155-165. | Zbl
, ,[20] Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964) 247-302. | MR | Zbl
,[21] On a class of semilinear elliptic problems with first order terms, Adv. Differential Equations 8 (2003) 257-278. | MR | Zbl
, ,[22] On positive solutions to a class of equations with singular coefficient and critical exponent, Adv. Differential Equations 1 (1996) 241-264. | MR | Zbl
,[23] The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, J. Funct. Anal. 173 (2000) 103-153. | MR | Zbl
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