Existence and Ulam Stability of Solution for Some Backward Impulsive Differential Equations on Banach Spaces

Abstract

In this paper, we study the existence and the Ulam stability of a solution to nonlinear backward impulsive differential equations with local or nonlocal conditions in Banach spaces. Using well-known classical fixed point theorems, we prove the existence of a solution. Subsequently, we prove the generalized Ulam-Hyers-Rassias stability of the solution to the problem. The obtained results are illustrated by some examples.