Author:
Chen Pengyu,Zhang Xuping,Zhang Zhitao
Abstract
<p style='text-indent:20px;'>In this paper, we investigate the global existence, uniqueness and asymptotic stability of time periodic classical solution for a class of extended Fisher-Kolmogorov equations with delays and general nonlinear term. We establish a general framework to investigate the asymptotic behavior of time periodic solutions for nonlinear extended Fisher-Kolmogorov equations with delays and general nonlinear function, which will provide an effective way to deal with such kinds of problems. The discussion is based on the theory of compact and analytic operator semigroups and maximal regularization method.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
Reference28 articles.
1. H. Amann, Periodic solutions of semilinear parabolic equations, in: L. Cesari, R. Kannan, R. Weinberger (Eds.), Nonlinear Analysis: Collection of Papers in Honor of Erich H. Rothe, Academic Press, New York, 1978, 1–29.
2. A. L. A. de Araujo.Periodic solutions for extended Fisher-Kolmogorov and Swift-Hohenberg equations obtained using a continuation theorem, Nonlinear Anal., 94 (2014), 100-106.
3. T. A. Burton, B. Zhang.Periodic solutions of abstract differential equations with infinite delay, J. Differential Equations, 90 (1991), 357-396.
4. T. A. Burton, Stability and Periodic Solutions of Ordinary Differential Equations and Functional Differential Equations, Academic Press, Orlando, FL, 1985.
5. A. Caicedo, C. Cuevas, G. M. Mophou, G. M. N'Guérékata.Asymptotic behavior of solutions of some semilinear functional differential and integro-differential equations with infinite delay in Banach spaces, J. Franklin Inst., 349 (2012), 1-24.