A second order differential inclusion with proximal normal cone in Banch spaces
Keywords
Differential inclusion, uniformly smooth Banach space, sweeping process, proximal normal coneAbstract
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 $K(x(t))$.Downloads
Published
2016-04-12
How to Cite
1.
ALIOUANE, Fatine and AZZAM-LAOUIR, Dalila. A second order differential inclusion with proximal normal cone in Banch spaces. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 44, no. 1, pp. 143 - 160. [Accessed 2 December 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0