Nonlinear delay reaction-diffusion systems with nonlocal initial conditions having affine growth

Abstract

We consider a class of abstract evolution reaction-diffusion systems with delay and nonlocal initial data of the formwhere τ i ≥ 0, i = 1, 2, A and B are two m-dissipative operators acting in two Banach spaces, the perturbations F and G are continuous, while the history functions p and q are nonexpansive functions with affine growth. We prove an existence result of C 0 -solutions for the above problem and we give an example to illustrate the effectiveness of our abstract theory.