Faedo-Galerkin approximation technique to non-instantaneous impulsive abstract functional differential equations

Abstract

This manuscript is devoted to the study of a class of nonlinear non-instantaneous impulsive first order abstract retarded type functional differential equations in an arbitrary separable Hilbert space H. A new set of sufficient conditions are derived to ensure the existence of approximate solutions. Finite dimensional approximations are derived using the projection operator. Through the utilization of analytic semigroup theory, fixed point theorem and Gronwall inequality, we establish the uniqueness and convergence of approximate solutions. Additionally, we study the Faedo-Galerkin approximate solutions and establish some convergence results. Finally, an illustrative instance demonstrating the applications of obtained results to partial differential equations is provided.