Existence and stability of solutions to nonlinear impulsive differential equations in beta-normed spaces

Abstract

In this article, we consider nonlinear impulsive differential equations in beta-normed spaces. We give new concepts of beta-Ulam's type stability. Also we present sufficient conditions for the existence of solutions for impulsive Cauchy problems. Then we obtain generalized beta-Ulam-Hyers-Rassias stability results for the impulsive problems on a compact interval. An example illustrates our main results.

Keywords

• Nonlinear impulsive differential equations
• existence
• stability