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Existence theorems forquasilinear multivalued boundary value problems in RN

Published online by Cambridge University Press:  13 November 2000

Nikolaos Kourogenis  and
Nikolaos S. Papageorgiou
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Abstract

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In this paper we study quasilinear second order boundary value problems with multivalued right hand side and Dirichlet boundary conditions. We prove three existence theorems. The first two deal with the “convex” and “nonconvex” problems respectively, while the third establishes the existence of extremal solutions. For the first two the proof is based on the theory of nonlinear operators of monotone type, while the proof of the third uses a fixed point argument.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 3 , September 2000 , pp. 359 - 369
Copyright
2000 Glasgow Mathematical Journal Trust