Impulsive hyperbolic differential inclusions with variable times
type: Item
instance of: scholarly article
title: Impulsive hyperbolic differential inclusions with variable times
zbMATH Open document ID: 1050.35159
DOI: 10.12775/TMNA.2003.042
published in: Topological Methods in Nonlinear Analysis
publication date: 2004-03-29T00:00:00Z
review text: The authors deal with the existence of solutions for the second-order impulsive hyperbolic differential inclusions with variable times \[ \begin{aligned} {\partial^2u\over\partial t\,\partial x}\in F(t,x,u(t,x))\quad\text{a.e. }(t,x)\in J_a\times J_b,&\quad t\neq \tau_k(u(t,x)),\\ u(t^+, x)= I_k(u(t,x)),&\quad t= \tau_k(u(t,x)),\\ u(t,0)= \psi(t),&\quad t\in J_a,\\ u(0,x)= \varphi(x),&\quad x\in J_b,\end{aligned} \] where \(F: J_a\times J_b\times \mathbb{R}^d\to P(\mathbb{R}^d)\) is a multivalued map with compact values, \(J= J_a\times J_b=\) \([0,a]\times [0,b]\), \(I_k\in C^1(\mathbb{R}^d,\mathbb{R}^d)\), \(\varphi\in C(J_a, \mathbb{R}^d)\), \(u(t^+,y):= \lim_{(h,x)\to (0^+,y)} u(t+ h,x)\), \(u(t^-,y):= \lim_{(h,x)\to (0^-,y)} u(t- h,x)\). To this end the authors use the nonlinear alternative of Leray-Schauder theory.
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35R12
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 2062968
zbMATH Keywords: impulsive hyperbolic differential inclusion
zbMATH Keywords: existence
zbMATH Keywords: multivalued map
zbMATH Keywords: nonlinear alternative of Leray-Schauder type
author: Mouffak Benchohra
author: Lech Górniewicz
author: Sotiris K. Ntouyas
author: Abdelghani Ouahab
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2062968