Some simple nonlinear PDE's without solutions

Haïm Brezis; Xavier Cabré

Bollettino dell'Unione Matematica Italiana (1998)

  • Volume: 1-B, Issue: 2, page 223-262
  • ISSN: 0392-4041

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Brezis, Haïm, and Cabré, Xavier. "Some simple nonlinear PDE's without solutions." Bollettino dell'Unione Matematica Italiana 1-B.2 (1998): 223-262. <http://eudml.org/doc/196173>.

@article{Brezis1998,
author = {Brezis, Haïm, Cabré, Xavier},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {blow-up; nonexistence result; inverse function theorem},
language = {eng},
month = {6},
number = {2},
pages = {223-262},
publisher = {Unione Matematica Italiana},
title = {Some simple nonlinear PDE's without solutions},
url = {http://eudml.org/doc/196173},
volume = {1-B},
year = {1998},
}

TY - JOUR
AU - Brezis, Haïm
AU - Cabré, Xavier
TI - Some simple nonlinear PDE's without solutions
JO - Bollettino dell'Unione Matematica Italiana
DA - 1998/6//
PB - Unione Matematica Italiana
VL - 1-B
IS - 2
SP - 223
EP - 262
LA - eng
KW - blow-up; nonexistence result; inverse function theorem
UR - http://eudml.org/doc/196173
ER -

References

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  1. BARAS, P.- COHEN, L., Complete blow-up after T max for the solution of a semilinear heat equation, J. Funct. Anal., 71 (1987), 142-174. Zbl0653.35037MR879705
  2. BARAS, P.- PIERRE, M., Singularités éliminables pour des équations semi-linéaires, Ann. Inst. Fourier, 34 (1984), 185-206. Zbl0519.35002MR743627
  3. BARAS, P.- PIERRE, M., Critère d'existence de solutions positives pour des équations semi-linéaires non monotones, Ann. Inst. Henri Poincaré, 2 (1985), 185-212. Zbl0599.35073MR797270
  4. BREZIS, H.- CAZENAVE, T.- MARTEL, Y.- RAMIANDRISOA, A., Blow-up for u t - Δ u = g u revisited, Ad. Diff. Eq., 1 (1996), 73-90. Zbl0855.35063MR1357955
  5. BREZIS, H.- STRAUSS, W. A., Semi-linear second-order elliptic equations in L 1 , J. Math. Soc. Japan, 25 (1973), 565-590. Zbl0278.35041MR336050
  6. BREZIS, H.- VÁZQUEZ, J. L., Blow-up solutions of some nonlinear elliptic problems, to appear. Zbl0894.35038MR1605678
  7. GALLOUËT, T.- MOREL, J.-M., Resolution of a semilinear equation in L^{1}, Proc. Royal Soc. Edinburgh, 96A (1984), 275-288. Zbl0573.35030MR760776
  8. KALTON, N. J.- VERBITSKY, I. E., Nonlinear equations and weighted norm inequalities, to appear. Zbl0948.35044MR1475688
  9. KATO, T., Schröedinger operators with singular potentials, Israel J. Math., 13 (1972), 135-148. Zbl0246.35025MR333833
  10. MARTEL, Y., Complete blow-up and global behaviour of solutions of u t - Δ u = g u , to appear. Zbl0914.35057
  11. MOREL, J.-M.- OSWALD, L., A uniform formulation for Hopf maximum principle (1985, unpublished preprint). 
  12. PERAL, I.- VÁZQUEZ, J. L., On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term, Arch. Rational Mech. Anal., 129 (1995), 201-224. Zbl0821.35080MR1328476
  13. ZHAO, Z., Green function for Schrödinger operator and conditional Feynman-Kac gauge, J. Math. Anal. Appl., 116 (1986), 309-334. Zbl0608.35012MR842803

Citations in EuDML Documents

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  1. Paolo Caldiroli, Roberta Musina, Stationary states for a two-dimensional singular Schrödinger equation
  2. Boumediene Abdellaoui, Ireneo Peral, The equation - Δ 𝑢 - λ 𝑢 | 𝑥 | 2 = | 𝑢 | 𝑝 + 𝑐 𝑓 ( 𝑥 ) : The optimal power
  3. Stanislav I Pohozaev, Alberto Tesei, Nonexistence of local solutions to semilinear partial differential inequalities
  4. Lorenzo D’Ambrosio, Hardy-type inequalities related to degenerate elliptic differential operators
  5. Nathalie Grenon, Existence results for semilinear elliptic equations with small measure data
  6. Boumediene Abdellaoui, Veronica Felli, Ireneo Peral, Existence and nonexistence results for quasilinear elliptic equations involving the p -Laplacian

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