Existence and Monotone Scheme for Time-Periodic Nonquasimonotone Reaction]Diffusion Systems: Application to Autocatalytic Chemistry

The article considers time-periodic reaction]diffusion systems. The reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions. Dirichlet and Robin boundary conditions are included. The existence of periodic solutions is shown under appropriate conditions. Monotone approximating sequences closing in on the solutions from above and below are constructed. Application to autocatalysis in chemistry is given.