Year: 2019
Author: Raoqing Ma, Shangzhi Li, Shangjiang Guo
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 4 : pp. 545–560
Abstract
In this paper, we deal with a diffusive predator-prey model with mixed boundary conditions, in which the prey population can escape from the boundary of the domain while predator population can only live in this area and can not leave. We first investigate the asymptotic behaviour of positive solutions and obtain a necessary condition ensuring the existence of positive steady state solutions. Next, we investigate the existence of positive steady state solutions by using maximum principle, the fixed point index theory, $L_p$-estimation, and embedding theorems, Finally, local stability and uniqueness are obtained by linear stability theory and perturbation theory of linear operators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.545
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 4 : pp. 545–560
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Mixed boundaries local stability uniqueness.