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Anti-periodic solutions for semilinear evolution equations

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
273
Issue
2
Identifiers
DOI: 10.1016/s0022-247x(02)00288-3

Abstract

Abstract 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 L 2 function. Furthermore, anti-periodic solutions for second-order equations are also studied.

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