Periodic solutions of parabolic systems with time delays. (English) Zbl 0967.35061
The author discusses the existence of maximal and minimal periodic solutions of a coupled system of parabolic equations with time delays and with nonlinear boundary conditions. The proof of the existence theorem is based on the method of upper and lower solutions and its associated monotone iterations. This method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic-parabolic system. An application is given to a competitor-competitor-mutualist model which consists of a coupled system of three reaction-diffusion equations with time delays.
Reviewer: V.Lakshmikantham (Melbourne/Florida)
MSC:
| 35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
| 35R10 | Partial functional-differential equations |
| 35K55 | Nonlinear parabolic equations |
| 35B10 | Periodic solutions to PDEs |
Keywords:
maximal and minimal periodic solutions; nonlinear boundary conditions; method of upper and lower solutions; monotone iterations; competitor-competitor-mutualist modelReferences:
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