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Periodic solutions of reaction diffusion systems in a half-space domain. (English) Zbl 1146.35305
Summary: This paper is concerned with the existence and stability of periodic solutions for reaction diffusion systems with nonlinear Neumann boundary conditions in a half-space domain. The approach to the problem is by the method of upper and lower solutions and the integral representation of its associated monotone iterations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iterative process in the same fashion as for parabolic initial boundary value problems. A sufficient condition for the stability of a periodic solution is given and an application is also given to a plankton allelopathic model from aquatic ecology.
MSC:
35B10Periodic solutions of PDE
35K57Reaction-diffusion equations
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35K60Nonlinear initial value problems for linear parabolic equations