EXISTENCE AND CONTROLLABILITY FOR NEUTRAL PARTIAL DIFFERENTIAL INCLUSIONS NONDENSELLY DEFINED ON A HALF-LINE

In this article, we study the existence of the integral solution to the neutral functional differential inclusion (d)/(dt )Dyt - AD(yt) - Lyt E F(t, yt), for a.e. t E J := [0, infinity), y(0) = phi E C-E = C([-r, 0]; E), r > 0,and the controllability of the corresponding neutral inclusion (d)/D-dt (yt) - AD(yt) - L-yt E F(t, y(t)) + B-u(t), for a.e. t E J, y(0) = phi E C-E,n a half-line via the nonlinear alternative of Leray-Schauder type for con-tractive multivalued mappings given by Frigon. We illustrate our results with applications to a neutral partial differential inclusion with diffusion, and to a neutral functional partial differential equation with obstacle constrains.