On global dynamics of reaction–diffusion systems at resonance. (September 2020)

• Record Type: Journal Article
• Authors: Kokocki, Piotr
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: Semiflow -- Invariant set -- Rybakowski–Conley index -- Resonance; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111901
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we use the homotopy invariants methods to study the global dynamics of the reaction–diffusion systems that are at resonance at infinity. Considering degrees of the resonance for the nonlinear perturbation we establish Landesman–Lazer type conditions and use them to express the Rybakowski–Conley index of the invariant set consisting of all bounded solutions. Obtained results are applied to study the existence of solutions connecting stationary points for the system of nonlinear heat equations.