Existence and stability of steady-state solutions of reaction-diffusion equations with nonlocal delay effect

A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady-state solutions are proved via studying an equivalent reaction-diffusion system without nonlocal and delay structure and applying local and global bifurcation theory. The global structure of the set of steady states is characterized according to type of nonlinearities and diffusion coefficient. Our general results are applied to diffusive logistic growth models and Nicholson's blowflies-type models.

Automated summary

This study focuses on a general reaction-diffusion equation with spatiotemporal delay and Dirichlet boundary condition. The existence and stability of positive steady-state solutions are proved through analyzing an equivalent system without nonlocal and delay structure and applying local and global bifurcation theory. The global structure of steady states is characterized based on the type of nonlinearities and diffusion coefficient, with applications to diffusive logistic growth models and Nicholson's blowflies-type models.