Diversities of periodic solutions for a class of ecological model

Abstract

We consider a nonautonomous predator-prey model with nonmonotonic functional response in the periodic environment. Some new sufficient conditions are obtained for the nonexistence of periodic solutions and the global existence of at least one or two positive periodic solutions. Our method is based on Mawhin's coincidence degree and novel estimation techniques for the priori bounds of unknown solutions. Some novel estimation techniques are employed for the priori bounds of unknown solutions to Lz = lNz, which are much different from the arguments used in the previous literature. Some applications are also presented to illustrate the feasibility and effectiveness of our main results. A conclusion ends this article. Mathematics Subject Classification (2000): Primary: 34C25; Secondary: 92D25, 92B05