Periodic solutions to a class of biological diffusion models with hysteresis effect. (February 2016)

• Record Type: Journal Article
• Authors: Wang, Yifu; Zheng, Jiashan
• Is Part Of: Nonlinear analysis. Volume 27(2016)
• Page Start: 297
• Page End: 311
• Publication Date: 2016-02
• Subjects: Hysteresis effect -- Predator–prey interactions -- Periodic solutions -- Leray–Schauder Theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.07.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with a class of biological models which consists of a nonlinear diffusion equation and a hysteresis operator describing the relationship between some variables of the equations. By the viscosity approach, we show the existence of periodic solutions of the problem under consideration. More precisely, with the help of the subdifferential operator theory and Leray–Schauder theorem, we show the existence of periodic solutions to the approximation problem and then obtain the solution of the original problem by using a passage-to-limit procedure.