A second order differential inclusion with proximal normal cone in Banch spaces
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Differential inclusion, uniformly smooth Banach space, sweeping process, proximal normal coneAbstrakt
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 $K(x(t))$.Pobrania
Opublikowane
2016-04-12
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1.
ALIOUANE, Fatine & AZZAM-LAOUIR, Dalila. A second order differential inclusion with proximal normal cone in Banch spaces. Topological Methods in Nonlinear Analysis [online]. 12 kwiecień 2016, T. 44, nr 1, s. 143–160. [udostępniono 3.7.2024].
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