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

This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form $$ddot{u}(t) in F(t,u(t),dot u(t))+H(t,u(t),dot u(t)),quad hbox{a.e. } t in [0,1],$$ where $F$ is a convex valued multifunction upper semicontinuous on $Eimes E$ 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 $F(t,x,y)subset Gamma_{1}(t)$, $H(t,x,y)subset Gamma_{2}(t)$, where the multifunctions $Gamma_{1},Gamma_{2}:[0,1] ightrightarrows E$ are uniformly Pettis integrable

A second order differential inclusion with proximal normal cone in Banch spaces

In the present paper we mainly consider the second order evolution inclusion with proximal normal cone: \begin{cases} -\ddot{x}(t)\in N_{K(t)}(\dot{x}(t))+F(t,x(t),\dot{x}(t)), \quad \textmd{a.e.}\\ \dot x(t)\in K(t),\\ x(0)=x_0,\quad\dot x(0)=u_0, \end{cases} \leqno{(*)} where $t\in I=[0,T]$, $E$ is a separable reflexive Banach space, $K(t)$ a ball compact and $r$-prox-regular subset of $E$, $N_{K(t)}(\cdot)$ the proximal normal cone of $K(t)$ and $F$ an u.s.c. set-valued mapping with nonempty closed convex values. First, we prove the existence of solutions of $(*)$. After, we give an other existence result of $(*)$ when $K(t)$ is replaced by $K(x(t))$

Existence results for delay second order differential inclusions

In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established

Nonconvex perturbations of second order maximal monotone differential inclusions

In this paper we prove the existence of solutions for a two point boundary value problem for a second order differential inclusion governed by a maximal monotone operator with a mixed semicontinuous perturbation