Bifurcation from infinity and multiplicity results for an elliptic system from biology

Article type: Research Article

Authors: Li, Chunqiu^{; *} | Peng, Zhen

Affiliations: Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang Province, 325035, P. R. China

Correspondence: [*] Corresponding author. E-mail: lichunqiu@wzu.edu.cn.

Abstract: This article is concerned with the bifurcation from infinity of the following elliptic system arising from biology −κΔu=λu+f(x,u)−v,−Δv=u−v, in a bounded domain Ω⊂RN. We regard this problem as a stationary problem of some reaction-diffusion system. By using a method of a pure dynamical nature, we will establish some multiplicity results on bifurcations from infinity for this system under an appropriate Landesman-Lazer type condition.

Keywords: Conley index, bifurcation from infinity, elliptic equation, parabolic equation

DOI: 10.3233/ASY-231839

Journal: Asymptotic Analysis, vol. 134, no. 3-4, pp. 413-436, 2023