Discontinuous semilinear differential equations and multiple valued maps
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- by Jeffrey Rauch PDF
- Proc. Amer. Math. Soc. 64 (1977), 277-282 Request permission
Abstract:
To treat boundary value problems with nonlinearity of the form $g(u)$ where $g \in L_\infty ^{{\text {loc}}}({\mathbf {R}})$ one must extend g to be multiple valued. Once this is done weak solutions are obtained.References
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H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973. MR 50 # 1060.
- P. J. McKenna and J. Rauch, Strongly nonlinear perturbations of nonnegative boundary value problems with kernel, J. Differential Equations 28 (1978), no. 2, 253–265. MR 491053, DOI 10.1016/0022-0396(78)90070-0
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris; Gauthier-Villars, Paris, 1969 (French). MR 0259693
- Walter A. Strauss, On weak solutions of semi-linear hyperbolic equations, An. Acad. Brasil. Ci. 42 (1970), 645–651. MR 306715
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 277-282
- MSC: Primary 35G30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0442453-6
- MathSciNet review: 0442453