Existence of solutions of quasilinear integrodifferential equations with nonlocal condition
type: Item
instance of: scholarly article
title: Existence of solutions of quasilinear integrodifferential equations with nonlocal condition
zbMATH Open document ID: 0976.45011
published in: Tokyo Journal of Mathematics
publication date: 2001-01-11T00:00:00Z
review text: The authors prove the existence and uniqueness of mild and classical solutions of the quasilinear abstract differential equation \[ du(t)/dt + Au(t)=f (t, u(t))\quad (t\in (0, a]) \] with the nonlocal condition \[ u (0) + g(t_1, t_2,\dots , t_p, u(t_1),\dots , u(t_p))=u_0 \] where \(-A\) is the infinitesimal generator of a \(C_0\)-semigroup in a Banach space \(X\), \(u_0\in X\) and \(f : [0, a] \times X\rightarrow X, f : [0, a]^p \times X^p\rightarrow X\) are given functions, and \[ 0\leq t_1\leq t_2\leq \dots \leq t_p\leq a. \] The main results of the paper are obtained by using \(C_0\)-semigroups and the Banach fixed point theorem.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1523377
zbMATH Keywords: quasilinear abstract differential equations
zbMATH Keywords: nonlocal problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: quasilinear integrodifferential equations
zbMATH Keywords: Banach space
author: Krishnan Balachandran
author: Kôichi Uchiyama
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1255958815
OpenAlex ID: W2076004349
DOI: 10.3836/TJM/1255958815
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description: scientific article; zbMATH DE number 1523377