Displaying similar documents to “Periodic problems and problems with discontinuities for nonlinear parabolic equations”

Existence of solutions for nonlinear parabolic problems

Nikolaos Halidias, Nikolaos S. Papageorgiou (1999)

Archivum Mathematicum

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We consider nonlinear parabolic boundary value problems. First we assume that the right hand side term is discontinuous and nonmonotone and in order to have an existence theory we pass to a multivalued version by filling in the gaps at the discontinuity points. Assuming the existence of an upper solution φ and of a lower solution ψ such that ψ ≤ φ , and using the theory of nonlinear operators of monotone type, we show that there exists a solution x ∈ [ ψ , φ ] and that the set of all such solutions is...