期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 380, 期 -, 页码 360-403出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2023.10.052
关键词
Quasi-periodic; Time delay; KAM; Singular perturbation
类别
This article employs the CWB method to construct quasi-periodic solutions for nonlinear delayed perturbation equations, and combines the techniques of Green's function estimate and the reducibility method in KAM theory to solve the linear equation, thus extending the applicability of the CWB method. As an application, it studies the positive quasi-periodic solutions for a class of Lotka-Volterra equations with quasi-periodic coefficients and time delay.
We employ the Craig-Wayne-Bourgain (CWB) method to construct quasi-periodic solutions for the nonlinear delayed perturbation equations. The linearized equation at each step of the iterations is a differentialdifference equation on the torus. We shall combine the techniques of Green's function estimate and the reducibility method in KAM theory to solve the linear equation, which generalizes the applicability of the CWB method. As an application, we study the positive quasi-periodic solutions for a class of Lotka-Volterra equations with quasi-periodic coefficients and time delay. (c) 2023 Elsevier Inc. All rights reserved.
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