Positive Solutions of a reaction-diffusion system with Dirichlet boundary condition
Bull. Korean Math. Soc.
Published online February 13, 2020
Zhan-Ping Ma and Shao-Wen Yao
Henan Polytechnic University
Abstract : In this article, we study a reaction-diffusion system with homogeneous Dirich-
let boundary conditions, which describing a three-species food chain model . Under
some conditions, the predator-prey subsystem (u1≡ 0) has a unique positive solution
(u2,u3). By using r1as a bifurcation parameter, a connected set of positive solutions
of our system bifurcating from semi-trivial solution set (r1,(0,u2,u3)) is obtained.
Results are obtained by the use of degree theory in cones and sub and super solution
techniques.
Keywords : Reaction-diffusion; Food chain model; Positive solutions; Bifurcation; Degree theory;
MSC numbers : 35K57; 35B32; 92D25
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