Description

• Title:
  A second order differential inclusion with proximal normal cone in Banch spaces
• Creator:
  Aliouane, Fatine;
  Azzam-Laouir, Dalila
• Description:
  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 $K(x(t))$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.04.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 44, No 1 (September 2014); 143 - 160;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.040/8154
• Subject:
  Differential inclusion;
  uniformly smooth Banach space;
  sweeping process;
  proximal normal cone;
  34A60;
  49J52;
  58C20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.040
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other