A note on positive non-constant steady-state solutions to a reaction–diffusion model - Dong, Wei; Wei, Zhongli; Pang, Changci (Applied mathematics and computation, 2010)
In the present paper, we investigate a reaction–diffusion system with feedback effect subject to the homogeneous Neumann boundary condition and study the positive steady-state solutions. We establish a priori estimates for positive steady-state solutions and derive some results for non-existence of positive non-constant steady-state solutions. Our analysis complements the existing results on this model.