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Journal of Function Spaces
Volume 2015 (2015), Article ID 810451, 7 pages
http://dx.doi.org/10.1155/2015/810451
Research Article

Positive Coexistence of Steady States for a Diffusive Ratio-Dependent Predator-Prey Model with an Infected Prey

Department of Mathematics, Korea University, 2511 Sejong-Ro, Sejong 339-700, Republic of Korea

Received 4 December 2014; Accepted 24 April 2015

Academic Editor: Henryk Hudzik

Copyright © 2015 Kwangjoong Kim and Inkyung Ahn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We examine a diffusive ratio-dependent predator-prey system with disease in the prey under homogeneous Dirichlet boundary conditions with a hostile environment at its boundary. We investigate the positive coexistence of three interacting species (susceptible prey, infected prey, and predator) and provide nonexistence conditions of positive solutions to the system. In addition, the global stability of the trivial and semitrivial solutions to the system is studied. Furthermore, the biological interpretation based on the result is also presented. The methods are employed from a comparison argument for the elliptic problem as well as the fixed-point theory as applied to a positive cone on a Banach space.