Periodic Solutions of Parabolic Systems with Nonlinear Boundary Conditions

This paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions. The approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial-boundary value problems. A sufficient condition for the stability of a periodic solution is also given. These results are applied to three model problems arising from chemical kinetics, ecology, and population biology