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Li, Shanbing; Liu, Sanyang; Wu, Jianhua; Dong, Yaying

Positive solutions for Lotka-Volterra competition system with large cross-diffusion in a spatially heterogeneous environment. (English) Zbl 1362.35133

Nonlinear Anal., Real World Appl. 36, 1-19 (2017).
Summary: In this paper, we study the stationary problem for the Lotka-Volterra competition system with cross-diffusion in a spatially heterogeneous environment. Although some sufficient conditions for the existence of positive solutions are obtained by using global bifurcation theory, the information for their structure is far from complete. In order to get better understanding of the competition system with cross-diffusion, we focus on the asymptotic behaviour of positive solutions and derive two shadow systems as the cross-diffusion coefficient tends to infinity, moreover, the structure of positive solutions of the limiting system is analysed. The result of asymptotic behaviour also reveals different phenomena from that studied in [Y.-X. Wang and W.-T. Li, Nonlinear Anal., Real World Appl. 14, No. 1, 224–245 (2013; Zbl 1317.92067)].

Cited in 15 Documents

MSC:

35J60 Nonlinear elliptic equations
92D25 Population dynamics (general)

Keywords:

Lotka-Volterra competition system; cross-diffusion; spatially heterogeneous environment

Citations:

Zbl 1317.92067
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Full Text: DOI

References:

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