Three boundary value problems for second order differential inclusions in Banach spaces

The paper studies, in the context of Banach spaces, the problem of three boundary conditions for both second order differential inclusions and second order ordinary differential equations. The results are obtained in several new settings of Sobolev-type spaces involving Bochner and Pettis integrals. Some classes of second order multivalued evolution equations associated with m-accretive operators are also considered. Applications to some control problems are provided with the help of narrow convergence for Young measures.