Existence and Ulam stability of solution for some backward impulsive differential equations on Banach spaces

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Submitted: 2024-12-06; Published: 2024-12-06

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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.