Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semi linear equations whose nonlinear terms do not contain delays.
- Differential inequalities
- Invariant sets
- Reaction-diffusion-delay systems
- Semilinear functional differential equations
ASJC Scopus subject areas
- Applied Mathematics