Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect

In this paper, the existence, stability, and multiplicity of spatially nonhomogeneous steady-state solution and periodic solutions for a reaction-diffusion model with nonlocal delay effect and Dirichlet boundary condition are investigated by using Lyapunov-Schmidt reduction. Moreover, we illustrate our general results by applications to models with a single delay and one-dimensional spatial domain. (C) 2015 Elsevier Inc. All rights reserved.