Anti-periodic solutions for semilinear evolution equations

In this paper, we study the existence problem of anti-periodic solutions for the following first-order nonlinear evolution equation: u′(t)+Au(t)+F(t,u(t))=0,t∈R,u(t+T)=−u(t),t∈R, in a Hilbert space H, where A is a self-adjoint operator and F is a continuous nonlinear operator. An existence result is...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 273; no. 2; pp. 627 - 636
Main Authors Chen, Yuqing, Wang, Xiangdong, Xu, Haixiang
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.09.2002
Elsevier
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Ordinary differential equations
Sciences and techniques of general use
Solution uniqueness
Second order equation
Semi linear equation
Antiperiodic solution
Differential equation
Bounded operator
Evolution equation
Linear operator
Equation system
Non linear equation
First order equation
Separable space
Hilbert space
Self adjoint operator
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Summary:In this paper, we study the existence problem of anti-periodic solutions for the following first-order nonlinear evolution equation: u′(t)+Au(t)+F(t,u(t))=0,t∈R,u(t+T)=−u(t),t∈R, in a Hilbert space H, where A is a self-adjoint 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 a L2 function. Furthermore, anti-periodic solutions for second-order equations are also studied.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(02)00288-3