Nonlinear second-order multivalued boundary value problems

Details Nonlinear second-order multivalued boundary value problems Nonlinear second-order multivalued boundary value problems

2003-10-17

arxiv.org/abs/math/0310264v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 293-319

Mathematics

Classical Analysis and ODEs

26 pages

Scientific paper

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.

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