Second order nonlinear multivalued boundary problems in Hilbert spaces

In this paper we consider second order differential inclusions in real Hilbert space, namely p(t)⋅x″(t)+r(t)⋅x′(t)∈Ax(t)+F(t,x(t)), a.e. on [0,T], under the nonlinear boundary conditions. Using techniques from multivalued analysis and the theory of operators of monotone type, we prove the existence of solutions for both the ‘convex’ and ‘nonconvex’ problems. Finally, we present a special case of interest, which fit into our framework, illustrating the generality of our results.