Nonexistence of nonconstant positive steady states of a diffusive predator-prey model

Shanshan Chen
2017 Communications on Pure and Applied Analysis  
In this paper, we investigate a diffusive predator-prey model with a general predator functional response. We show that there exist no nonconstant positive steady states when the interaction between the predator and prey is strong. This result implies that the global bifurcating branches of steady state solutions are bounded loops for a predator-prey model with Holling type III functional response. 2000 Mathematics Subject Classification. Primary: 35K57; Secondary: 35B36.
doi:10.3934/cpaa.2018026 fatcat:veqgradffnbchmwz6owsp4qooa