Anti-periodic solutions for semilinear evolution equations.
type: Item
instance of: scholarly article
title: Anti-periodic solutions for semilinear evolution equations.
zbMATH Open document ID: 1055.34113
DOI: 10.1016/S0022-247X(02)00288-3
author: Haixiang Xu
author: Yuqing Chen
author: Xiangdong Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The authors study the existence problem of anti-periodic solutions for the following first-order nonlinear evolution equation \[ \begin{cases} u'(t)+Au(t)+F(t,u(t))=0, &t\in\mathbb R\\ u(t+T)=-u(t), &t\in\mathbb R,\end{cases} \] in a Hilbert space \(H\), where \(A\) is a selfadjoint operator and \(F\) is a continuous nonlinear operator. An existence result is obtained under assumptions that \(D(A)\) is compactly embedded into \(H\) and \(F\) is anti-periodic and bounded by an \(L^2\) function. Furthermore, anti-periodic solutions for second-order equations are also studied.
reviewed by: J. N. Pandey
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1866589
MaRDI profile type: Publication
cites work: On a class of second-order anti-periodic boundary value problems
cites work: Anti-periodic boundary value problems for higher order differential equations in Hilbert spaces
cites work: Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space
cites work: Q4254447
cites work: Periodic solutions of a nonlinear wave equation without assumption of monotonicity
cites work: Q3678037
cites work: Nonlinear evolution equations - global behavior of solutions
cites work: Anti-periodic solutions of some nonlinear evolution equations
cites work: On the existence of periodic solutions to nonlinear abstract parabolic equations
cites work: On the existence of anti-periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators
cites work: Q5667036
description: scientific article; zbMATH DE number 1866589