Positive steady-state solutions for predator–prey systems with prey-taxis and Dirichlet conditions. (December 2022)

• Record Type: Journal Article
• Authors: Li, Shanbing; Ma, Ruyun
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Predator–prey system -- Prey-taxis -- Positive steady-state solutions -- Limiting behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103669
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with positive steady-state solutions of a class of cross-diffusion systems which arise in the study of the predator–prey systems with prey-taxis. Under homogeneous Dirichlet boundary conditions, we use the theory of fixed point index in positive cones to establish the existence of positive steady-state solutions. By analyzing two related eigenvalues, we further obtain the coexistence region with respect to the growth rates of two species and characterize the differences of coexistence region if different predator–prey interactions are adopted. Additionally, we investigate the limiting behavior of positive steady-state solutions as some parameter tends to infinity. Our results not only generalize the previously known one, but also present some new conclusions.