Journal of Function Spaces (Jan 2019)
Fixed Point Theory and Positive Solutions for a Ratio-Dependent Elliptic System
Abstract
We consider a ratio-dependent predator-prey model under zero Dirichlet boundary condition. By using topological degree theory and fixed index theory, we study the necessary and sufficient conditions for the existence of positive solutions. Then we present the asymptotic behavior analysis of positive solutions, by bifurcation theory and energy estimates.