Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations
- 1 November 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 17 (6) , 1339-1353
- https://doi.org/10.1137/0517094
Abstract
In this paper the structure of the nonnegative steady-state solutions of a system of reaction-diffusion equations arising in ecology is investigated. The equations model a situation in which a predator species and a prey species inhabit the same region and the interaction terms are of Holling–Tanner type sothat the predator has finite appetite. Prey and predator birth-rates are treated as bifurcation parameters and the theorems of global bifurcation theory are adapted so that they apply easily to the system. Thus ranges of parameters are found for which there exist nontrivial steady-state solutions.Keywords
This publication has 9 references indexed in Scilit:
- On positive solutions of some pairs of differential equationsTransactions of the American Mathematical Society, 1984
- Bifurcation of steady-state solutions in predator-prey and competition systemsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984
- Monotone schemes for semilinear elliptic systems related to ecologyMathematical Methods in the Applied Sciences, 1982
- Methods of Bifurcation TheoryPublished by Springer Nature ,1982
- Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach SpacesSIAM Review, 1976
- Topics in Stability and Bifurcation TheoryPublished by Springer Nature ,1973
- Bifurcation from simple eigenvaluesJournal of Functional Analysis, 1971
- Some global results for nonlinear eigenvalue problemsJournal of Functional Analysis, 1971
- Nonlinear boundary value problems suggested by chemical reactor theoryJournal of Differential Equations, 1970