Nonlinear Second-Order Multivalued Boundary Value Problems

[摘要] 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 operatory 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.

[学科分类] 数学（综合）

[关键词] Maximal monotone operator;pseudomonotone operator;Hartman condition;vector 𝑝-Laplacian;convex and nonconvex problems;Leray–Schauder alternative.