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Discontinuous semilinear differential equations and multiple valued maps. (English) Zbl 0413.35031


MSC:

35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35K55 Nonlinear parabolic equations
35L60 First-order nonlinear hyperbolic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35R05 PDEs with low regular coefficients and/or low regular data
35J65 Nonlinear boundary value problems for linear elliptic equations
35L70 Second-order nonlinear hyperbolic equations
54C60 Set-valued maps in general topology
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References:

[1] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973. MR 50 # 1060. · Zbl 0252.47055
[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. · Zbl 0405.34019
[3] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969 (French). · Zbl 0189.40603
[4] Walter A. Strauss, On weak solutions of semi-linear hyperbolic equations, An. Acad. Brasil. Ci. 42 (1970), 645 – 651. · Zbl 0217.13104
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