Differential and Integral Equations
- Differential Integral Equations
- Volume 8, Number 2 (1995), 371-391.
On the fixed point index and multiple steady-state solutions of reaction-diffusion systems
This paper is concerned with the fixed point index of a compact operator and its application to the study of multiple steady-state solutions of nonlinear reaction-diffusion systems. The method is simplified under the condition that the Banach space $X$ can be decomposed as $X=Y\oplus S_\varphi$, which is frequently satisfied by various reaction-diffusion models. A new method for proving the existence of positive steady-state solutions is developed by using this simplified method to semiflows. The result is applied to a three-species ecological model for which some sufficient conditions for the existence of positive steady-state solutions are obtained.
Differential Integral Equations, Volume 8, Number 2 (1995), 371-391.
First available in Project Euclid: 20 May 2013
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Ruan, Weihua; Feng, Wei. On the fixed point index and multiple steady-state solutions of reaction-diffusion systems. Differential Integral Equations 8 (1995), no. 2, 371--391. https://projecteuclid.org/euclid.die/1369083475