On the existence of solutions for a class of second-order differential inclusions and applications

In this paper, by extending the method of guiding functions, we give sufficient conditions for the existence of solutions to the problem(1.1) u ″ ∈ Q ( u ) , u ( 0 ) = u ( 1 ) = 0 , where Q is a multivalued map whose values are not necessarily convex. It is shown how abstract results can be applied to study feedback control systems and to describe a motion of a particle in a 1-D potential.