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Proceedings of the American Mathematical Society

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

 

 

Discontinuous semilinear differential equations and multiple valued maps


Author: Jeffrey Rauch
Journal: Proc. Amer. Math. Soc. 64 (1977), 277-282
MSC: Primary 35G30
MathSciNet review: 0442453
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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 [Enhancements On Off] (What's this?)

  • [1] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973. MR 50 # 1060.
  • [2] 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, 10.1016/0022-0396(78)90070-0
  • [3] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969 (French). MR 0259693
  • [4] Walter A. Strauss, On weak solutions of semi-linear hyperbolic equations, An. Acad. Brasil. Ci. 42 (1970), 645–651. MR 0306715

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DOI: https://doi.org/10.1090/S0002-9939-1977-0442453-6
Article copyright: © Copyright 1977 American Mathematical Society