Structure of the solution set for a partial differential inclusion

Abstract

In this paper, we consider the biharmonic problem of a partial differential inclusion with Dirichlet boundary conditions. We prove existence theorems for related partial differential inclusions with convex and nonconvex multivalued perturbations, and obtain an existence theorem on extremal solutions, and a strong relaxation theorem. Also we prove that the solution set is compact R-delta if the perturbation term of the related partial differential inclusion is convex, and its solution set is path-connected if the perturbation term is nonconvex.