Nonlinear multivalued boundary value problems

Ralf Bader; Nikolaos Papageorgiou

ArticleOriginal scientific text

Title

Nonlinear multivalued boundary value problems

Authors ¹, ²

Affiliations

Center of Mathematics, Technical University Muenchen, Arcisstr. 21, D-80333 Muenchen, Germany
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

Abstract

In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when

d o m A \neq ℝ^{N}

and

d o m A = ℝ^{N}

, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.

Keywords

ENG

usc and lsc multifunction, measurable selection, Leray-Schauder alternative theorem, Sobolev space, compact embedding, maximal monotone map, coercive map, surjective map, convex and nonconvex problem, nonlinear boundary conditions

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Title

Nonlinear multivalued boundary value problems

Affiliations

Abstract

Keywords

Bibliography