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Periodic solutions of a single species renewable resources under periodic habitat fluctuations with harvesting and Allee effects. (English) Zbl 1295.34055

Summary: The authors study the existence of at least two positive periodic solutions of the dynamics of a single species renewable resource under periodic habitat fluctuation with harvesting and Allee effects.
They focus on two cases: 1. Proving existence of two positive periodic solutions of a differential equation that has an unbounded Green’s kernel, and 2. Applying these results to find the existence of two positive periodic solutions of a model with Allee effects and harvesting. The results obtained are new and improve some existing results.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C25 Periodic solutions to ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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