TY - JOUR AU - Cheng, Yi AU - Agarwal, Ravi P. AU - Ben Amar, Afif AU - O’Regan, Donal PY - 2015 DA - 2015/12/18 TI - Structure of the solution set for a partial differential inclusion JO - Advances in Difference Equations SP - 380 VL - 2015 IS - 1 AB - 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. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-015-0723-0 DO - 10.1186/s13662-015-0723-0 ID - Cheng2015 ER -