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Periodic solutions of a class of degenerate parabolic system with delays. (English) Zbl 1217.35014

Summary: This paper is concerned with a class of periodic degenerate parabolic system with time delays in a bounded domain under mixed boundary condition. Under locally Lipschitz conditions on reaction functions, we apply the Schauder fixed point theorem to obtain the existence of periodic solutions of the periodic problem. With quasi-monotonicity in addition, we also show that the periodic problem has a maximal and a minimal periodic solutions. Applications of the obtained results are also given to some nonlinear diffusion models arising from ecology.

MSC:

35B10 Periodic solutions to PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K65 Degenerate parabolic equations
35R10 Partial functional-differential equations
92D40 Ecology
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