Application of Pettis integration to differential inclusions with three-point boundary conditions in Banach spaces

Abstract

This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form ü(t) ∈ F(t, u(t), u̇(t)) + H(t, u(t), u̇(t)), a.e. t ∈ [0, 1], where F is a convex valued multifunction upper semicontinuous on E x E and H is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction H, and the assumption that F(t, x, y) ⊂ Γ1(t), H(t, x, y) ⊂ Γ2(t), where the multifunctions Γ1, Γ2 : [0, 1] ⇉ E are uniformly Pettis integrable.