Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side.
type: Item
instance of: scholarly article
title: Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side.
zbMATH Open document ID: 1034.45009
DOI: 10.1016/S0022-247X(03)00138-0
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: The authors study the following initial value problems for functional integro-differential inclusions: (1) \(y'(t)\in F( t,y_t, \int_0^t k(t,s,y_s)\,ds)\), a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\); (2) \(y''(t)\in F( t,y_t, \int_0^t k(t,s,y_s)\,dx)\), a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\), \(y'(0)= \eta\) (3) \(\frac{d}{dt} [y(t)-g(t,y_t)]\in F( t,y_t, \int_0^t k(t,s,y_s)\,ds)\), a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\), (4) \(\frac{d}{dt} [y'(t)- g(t,y_t)]\in F( t,y_t, \int_0^t k(t,s,y_s)\,ds)\) , a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\), \(y'(0)= \eta\). By means of suitable fixed point theorems existence results are obtained.
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 1956879
zbMATH Keywords: functional integrodifferential inclusions
zbMATH Keywords: selection
zbMATH Keywords: fixed point
author: Mouffak Benchohra
author: Efrosini P. Gatsori
author: Sotiris K. Ntouyas
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
cites work: Existence results for functional differential and integrodifferential inclusions in Banach spaces
cites work: Q5428788
cites work: Q4948671
cites work: Existence results on infinite intervals for neutral functional-differential and integrodifferential inclusions in Banach spaces
cites work: Extensions and selections of maps with decomposable values
cites work: Q4000472
cites work: Q4323870
cites work: Q3356948
cites work: Q3836181
cites work: Q3860165
cites work: Q4867184
cites work: Q4367585
cites work: Q4073972
cites work: Q4236992
cites work: Q4051163
cites work: A theorem on the existence of an optimal control for the Goursat-Darboux problem without convexity assumptions
description: scientific article; zbMATH DE number 1956879