Existence results for a self-adjoint coupled system of nonlinear second-order ordinary differential inclusions with nonlocal integral boundary conditions

Abstract

Abstract A coupled system of nonlinear self-adjoint second-order ordinary differential inclusions supplemented with nonlocal nonseparated coupled integral boundary conditions on an arbitrary domain is studied. The existence results for convex and nonconvex valued maps involved in the given problem are proved by applying the nonlinear alternative of Leray–Schauder for multivalued maps and Covitz–Nadler’s fixed point theorem for contractive multivalued maps, respectively. Illustrative examples for the obtained results are presented. The paper concludes with some interesting observations.

Keywords

• Self-adjoint ordinary differential inclusions
• Coupled
• Nonlocal integral boundary conditions
• Existence
• Fixed point