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Nonlinear Boundary Value Problems for Second Order Differential Inclusions
Authors:Sophia Th. Kyritsi  Nikolaos Matzakos  Nikolaos Papageorgiou
Affiliation:(1) Dept. of Mathematics, National Technical University, Zografou Campus, Athens, 157 80, Greece
Abstract:In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form xa(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝN. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side.
Keywords:measurable multifunction  usc and lsc multifunction  maximal monotone operator  pseudomonotone operator  generalized pseudomonotone operator  coercive operator  surjective operator  eigenvalue  eigenfunction  Rayleigh quotient   p-Laplacian  Yosida approximation  periodic problem
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