Differential and Integral Equations

On the fixed point index and multiple steady-state solutions of reaction-diffusion systems

Wei Feng and Weihua Ruan

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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.

Article information

Differential Integral Equations, Volume 8, Number 2 (1995), 371-391.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 47H11: Degree theory [See also 55M25, 58C30] 47N20: Applications to differential and integral equations


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

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