Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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EXISTENCE OF POSITIVE SOLUTIONS OF PREDATOR-PREY SYSTEMS WITH DEGENERATE DIFFUSION RATES

  • Ryu, Kimun (Department of Mathematics Education, Cheongju University)
  • Received : 2019.12.13
  • Accepted : 2019.12.30
  • Published : 2020.02.15
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Abstract

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

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Acknowledgement

The author thanks the anonymous referees for their valuable comments and suggestions to improve the content of this article.

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