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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
    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
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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