On a Class of Nonlinear Reaction-diffusion Systems with Nonlocal Boundary Conditions

In the recent years, a new attention has been given to reaction-diffusion systems which involve an integral over the spatial domain of a function of the desired solution on the boundary conditions; see [2, 5, 7, 6, 9, 10, 17, 18, 19, 20, 22] and the references cited therein. Most of the studied problems in the current literature are devoted to problems which combine a classical boundary condition (Dirichlet, Neumann, etc.) with an integral condition for single linear equations. The purpose of this paper is to prove the existence and uniqueness of a solution for the following nonlinear reaction-diffusion system with only integral conditions: