Boundary value problem for differential inclusions in Frechet spaces with multiple solutions of the homogeneous problem

The paper deals with the multivalued boundary value problem x 0 2 A(t, x)x+ F(t, x) for a.a. t 2 (a, b), Mx(a) + Nx(b) = 0, in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x. We prove the existence of global solutions in the Sobolev space W 1,p ((a, b), E) with 1 < p < 1 endowed with the weak topol- ogy. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion.