Existence of periodic traveling waves in a nonlocal convection-diffusion model with chemotaxis and delay effect

We focus upon the existence of periodic traveling waves in a nonlocal reaction-diffusion model with chemotaxis and nonlocal delay effect. Based on the perturbation method, the existence of periodic traveling waves with large wave speed are obtained by the Lyapunov-Schmidt reduction and the implicit function theorem. The trick of the proof is to treat the wave profile as a solution of an operator in a suitable Banach space. Mathematics Subject Classification (2000) 35K57 · 34K05