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

Zhao, Xiao-Qiang

Can. Appl. Math. Q. 17, No. 1, 271-281 (2009).

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.

Reviewer: Laura Iulia Aniţa (Iaşi)

MSC:

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

Keywords:

diffusion; delay; extinction and persistence; global attractivity; positive steady state; Neumann boundary conditions; fluctuation method