Positive Steady-state Solutions of a Non-linear Reaction-Diffusion System
Hongwei Chen · Mathematical Methods in the Applied Sciences · 1997
The steady-state problem of the non-linear reaction-diffusion system ut−uxx=u(av−b) , vt−vxx=cu is considered. The existence of positive steady-solutions is established by using a fixed point theorem in ordered Banach space. The uniqueness of ordered positive steady-state solutions and an application to the associated reaction-diffusion system are presented. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.