Abstract
In this paper we consider a general nonlinear boundary value problem for second-order differential inclusions. We prove two existence theorems, one for the ``convex'' problem and the other for the ``nonconvex'' problem. Then we show that the solution set of the latter is dense in the C 1 (T,R N ) -norm to the solution set of the former (relaxation theorem). Subsequently for a Dirichlet boundary value problem we prove the existence of extremal solutions and we show that they are dense in the solutions of the convexified problem for the C 1 (T,R N ) -norm . Our tools come from multivalued analysis and the theory of monotone operators and our proofs are based on the Leray—Schauder principle.
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