Nonlinear boundary value problems for differential inclusions

In this paper we study nonlinear second order scalar differential inclusions with nonlinear multivalued boundary conditions. Assuming the existence of an ordered pair of upper and lower solutions, we establish the existence of a solution in the order interval formed by them. Our approach uses the tools of multivalued analysis and of the theory of nonlinear operators of monotone type. The problem studied here has as special cases the Dirichlet, Neumann and Sturm-Liouville problems. Also we show that the same approach can be used in the study of the periodic problem.