Geodesic
Nonlinear multivalued boundary value problems
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 1, pp. 127-148.

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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.
Keywords: 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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Bader, Ralf; Papageorgiou, Nikolaos. Nonlinear multivalued boundary value problems. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 1, pp. 127-148. http://geodesic.mathdoc.fr/item/DMDICO_2001_21_1_a4/

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