SOLUTION OF THE PARTIAL NEUTRAL FUNCTION DIFFERENTIAL EQUATION WITH THE LINEAR PART SATISFYING THE HILLE - YOSIDA CONDITION

Abstract

In this paper, we study the existence of solution for semi-linear partial neutral functional differential equations with the linear part satisfies the Hille - Yosida condition and the nonlinear delay operator satisfies the Lipschitz condition. In the case of the evolution family have an exponential dichotomy, we construct the Lyapunov - Perron solution formula and prove the existence of the solution.