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2001 | 21 | 1 | 127-148
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Nonlinear multivalued boundary value problems

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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 $domA ≠ ℝ^{N}$ and $domA = ℝ^{N}$, 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.
  • Center of Mathematics, Technical University Muenchen, Arcisstr. 21, D-80333 Muenchen, Germany
  • National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
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