Nonexistence of local solutions to semilinear partial differential inequalities

Stanislav I Pohozaev; Alberto Tesei

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 4, page 487-502
  • ISSN: 0294-1449

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Pohozaev, Stanislav I, and Tesei, Alberto. "Nonexistence of local solutions to semilinear partial differential inequalities." Annales de l'I.H.P. Analyse non linéaire 21.4 (2004): 487-502. <http://eudml.org/doc/78626>.

@article{Pohozaev2004,
author = {Pohozaev, Stanislav I, Tesei, Alberto},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonexistence; local solutions; instantaneous blowup; semilinear elliptic inequalities},
language = {eng},
number = {4},
pages = {487-502},
publisher = {Elsevier},
title = {Nonexistence of local solutions to semilinear partial differential inequalities},
url = {http://eudml.org/doc/78626},
volume = {21},
year = {2004},
}

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
PB - Elsevier
VL - 21
IS - 4
SP - 487
EP - 502
LA - eng
KW - nonexistence; local solutions; instantaneous blowup; semilinear elliptic inequalities
UR - http://eudml.org/doc/78626
ER -

References

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  1. [1] Brezis H, Cabré X, Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital.1-B (1998) 223-262. Zbl0907.35048MR1638143
  2. [2] Brezis H, Cazenave T, Martel Y, Ramiandrisoa A, Blow up for ut−Δu=g(u) revisited, Adv. Differential Equations1 (1996) 73-90. Zbl0855.35063
  3. [3] Brezis H, Vazquez J.L, Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Compl. Madrid10 (1997) 443-469. Zbl0894.35038MR1605678
  4. [4] Cabré X, Martel Y, Weak eigenfunctions for the linearization of extremal elliptic problems, J. Funct. Anal.156 (1998) 30-56. Zbl0908.35044MR1632972
  5. [5] Cabré X, Martel Y, Existence versus explosion instantanée pour des equations de la chaleur linéaires avec potentiel singulier, C. R. Acad. Sci. Paris329 (1999) 973-978. Zbl0940.35105MR1733904
  6. [6] Caffarelli L, Gidas B, Spruck J, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math.42 (1989) 271-297. Zbl0702.35085MR982351
  7. [7] Dautray R, Lions J.L, Mathematical Analysis and Numerical Methods for Science and Technology, vol. I, Springer, 1985. Zbl0683.35001
  8. [8] Galakhov E, Some nonexistence results for quasilinear elliptic problems, J. Math. Anal. Appl.252 (2000) 256-277. Zbl0970.35070MR1797855
  9. [9] Dupaigne L, A nonlinear elliptic PDE with the inverse square potential, J. Anal. Math.86 (2002) 359-398. Zbl1034.35043MR1894489
  10. [10] Gidas B, Spruck J, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1981) 525-598. Zbl0465.35003MR615628
  11. [11] Holcman D, Nonlinear PDE with vector fields, J. Anal. Math.81 (2000) 111-137. Zbl0963.35054MR1785279
  12. [12] Joseph D.D, Lundgren T.S, Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal.49 (1973) 241-269. Zbl0266.34021MR340701
  13. [13] Korevaar N, Mazzeo R, Pacard F, Schoen R, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math.135 (1989) 233-272. Zbl0958.53032MR1666838
  14. [14] Mitidieri E, Pohozaev S.I, The absence of global positive solutions to quasilinear elliptic inequalities, Dokl. Russ. Acad. Sci.359 (1998) 456-460. Zbl0976.35100MR1668404
  15. [15] Mitidieri E, Pohozaev S.I, 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. Zbl1074.35500MR1879326
  16. [16] Moschini L, Pohozaev S.I, Tesei A, Existence and nonexistence of solutions of nonlinear Dirichlet problems, J. Funct. Anal.177 (2000) 365-382. Zbl0976.35025MR1795956
  17. [17] Moschini L, Pohozaev S.I, Tesei A, On a class of nonlinear Dirichlet problems with first order terms, in: International Conference on Differential and Functional Differential Equations, Moscow, 1999, Funct. Differ. Equations8 (2001) 345-352. Zbl1098.35555MR1950978
  18. [18] Pohozaev S.I, Tesei A, Blow-up of nonnegative solutions to quasilinear parabolic inequalities, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.11 (2000) 99-109. Zbl1007.35003MR1797514
  19. [19] Pohozaev S.I, Tesei A, Instantaneous blow-up of solutions to a class of hyperbolic inequalities, Electronic J. Differential EquationsConference 08 (2002) 155-165. Zbl1024.35081
  20. [20] Serrin J, Local behavior of solutions of quasi-linear equations, Acta Math.111 (1964) 247-302. Zbl0128.09101MR170096
  21. [21] Smets D, Tesei A, On a class of semilinear elliptic problems with first order terms, Adv. Differential Equations8 (2003) 257-278. Zbl1290.35129MR1948046
  22. [22] Terracini S, On positive solutions to a class of equations with singular coefficient and critical exponent, Adv. Differential Equations1 (1996) 241-264. Zbl0847.35045MR1364003
  23. [23] Vazquez J.L, Zuazua E, The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, J. Funct. Anal.173 (2000) 103-153. Zbl0953.35053MR1760280

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