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Multiplicity and Uniqueness of Positive Solutions for a Predator–Prey Model with C–M Functional Response

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Abstract

In this paper, we are concerned with positive solutions of a predator–prey model with Crowley–Martin functional response under homogeneous Dirichlet boundary conditions. First of all, we state some known results and give the existence of positive solutions. Furthermore, the effect of large α is extensively studied. By analyzing the asymptotic behaviors of positive solutions when α goes to ∞, we derive a complete understanding of the multiplicity, uniqueness and stability of positive solutions.

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Acknowledgements

The authors would like to express their sincere thanks to the anonymous referees for their valuable suggestions which led to the improved presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710069, P.R. China

    Yaying Dong

  2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, P.R. China

    Shanbing Li & Yanling Li

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  1. Yaying Dong
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  2. Shanbing Li
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  3. Yanling Li
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Correspondence to Shanbing Li.

Additional information

The work is supported by the Natural Science Foundation of China (11271236, 11371293), the Program for New Century Excellent Talents in University of Ministry of Education of China (NCET-12-0894), the Fundamental Research Funds for the central Universities (GK201303008, GK201302025, GK201401004).

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Dong, Y., Li, S. & Li, Y. Multiplicity and Uniqueness of Positive Solutions for a Predator–Prey Model with C–M Functional Response. Acta Appl Math 139, 187–206 (2015). https://doi.org/10.1007/s10440-014-9985-x

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  • DOI: https://doi.org/10.1007/s10440-014-9985-x

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