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Global attractivity in a class of nonmonotone reaction-diffusion equations with time delay. (English) Zbl 1213.35119

The paper is devoted to the proof of the global attractivity of the positive steady state under appropriate assumptions for a class of nonmonotone time-delayed reaction-diffusion equations subject to Neumann boundary conditions, using a fluctuation method. Three examples from population dynamics are presented to illustrate the applicability of the main result.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
35R10 Partial functional-differential equations
92D25 Population dynamics (general)
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