×

Equations d’évolution avec non linearite logarithmique. (French) Zbl 0411.35051


MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L05 Wave equation
35A25 Other special methods applied to PDEs
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML

References:

[1] J.B. Baillon , T. Cazenave , M. Figueira . Equation de Schrödinger non linéaire . C.R. Acad. Sc. Paris , 284 ( 1977 ) p. 869 - 872 . MR 433025 | Zbl 0349.35048 · Zbl 0349.35048
[2] I. Bialynicki-Birula , J. Mycielski . Wave Equations with Logarithmic Non-linearities . Bull. Acad. Pol. Sc. , XXIII ( 1975 ) p. 461 - 466 . MR 403458
[3] I. Bialynicki-Birula , J. Mycielski . Nonlinear Wave Mechanics . Annals of Physics , 100 ( 1976 ) p. 62 - 93 . MR 426670
[4] H. Brezis . Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert . North-Holland Publish Co , Amsterdam , London ( 1973 ). MR 348562 | Zbl 0252.47055 · Zbl 0252.47055
[5] H. Brezis , T. Kato . Remarks on the Schrödinger Operator with Singular Complex Potentials . J. Math. Pures. Appl. 58 ( 1979 ) p. 137 - 151 . MR 539217 | Zbl 0408.35025 · Zbl 0408.35025
[6] F.E. Browder . On Non-Linear Wave Equations . Math. Zeitschr. 80 ( 1962 ) p. 249 - 264 . Article | MR 147769 | Zbl 0109.32102 · Zbl 0109.32102
[7] T. Cazenave . Equations de Schrödinger Non Linéaires . Proc. Roy. Soc. Edinburgh (1969) 84 ( 1979 ) p. 327 - 346 . MR 559676 | Zbl 0428.35021 · Zbl 0428.35021
[8] T. Cazenave , A. Haraux . Equations de Schrödinger avec Non Linéarité Logarithmique . C.R. Acad. Sc. Paris , 288 ( 1979 ) p. 253 - 256 . MR 524786 | Zbl 0406.35013 · Zbl 0406.35013
[9] R. Cou Rant , D. Hilbert . Methods of Mathematical Physics . Volume II , Inter-science Publish. New-York , London ( 1962 ). MR 65391 | Zbl 0099.29504 · Zbl 0099.29504
[10] J. Ginibre , G. Velo . On a class of Non Linear Schrödinger Equations . J. Funct. Anal. 32 ( 1979 ) p. 1 - 71 . MR 533219 | Zbl 0396.35028 · Zbl 0396.35028
[11] J.L. Lions . Quelques Méthodes de Résolution de Problèmes aux Limites Non-Linéaires . Gauthier-Villars , Paris ( 1969 ). MR 259693 | Zbl 0189.40603 · Zbl 0189.40603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.