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- Title
The existence of positive steady-state solutions for a predator-prey model.
- Authors
XU Juan; LI Yan-ling
- Abstract
The positive equilibrium solution exists of a Holling-]V type predator-prey model with homo-geneous Dirichlet boundary condition is concerned in this paper. First, the model is equivalent to an ellip-tic boundary problem to make a priori estimate of positive solutions. Then, by using the degree theory, calculating the index of the fixed point of the compact map in cone and combining with the operator spec-trum analysis, some sufficient conditions for the existence of positive equilibrium solutions are obtained. The result shows that the existence of the positive solution is closely related to the eigenvalues of differ-ential operators derived from the model.
- Subjects
EXISTENCE theorems; PREDATION; MATHEMATICAL models; BOUNDARY value problems; TOPOLOGICAL degree; DIFFERENTIAL operators; EIGENVALUES
- Publication
Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao, 2012, Vol 25, Issue 2, p149
- ISSN
1006-8341
- Publication type
Article