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 ⊕ Sφ, 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. © 1995, Khayyam Publishing.
Differential and Integral Equations
Ruan, W., Feng, W., & Goldstein, J. (1995). On the fixed point index and multiple steady-state solutions of reaction-diffusion systems. Differential and Integral Equations, 8 (2), 371-391. Retrieved from https://digitalcommons.memphis.edu/facpubs/5347