<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System

• Main Authors: Xiaoming Wang, Muhammad Arif, Akbar Zada
• Format: Article
• Language: English
• Published: MDPI AG 2019-02-01
• Series: Symmetry
• Subjects: semilinear nonautonomous system; instantaneous impulses; mild solution; <i>β</i>–Hyers–Ulam– Rassias stability
• Online Access: https://www.mdpi.com/2073-8994/11/2/231
• ISSN: 2073-8994

In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the <inline-formula> <math display="inline"> <semantics> <mi>&#946;</mi> </semantics> </math> </inline-formula>&#8315;Ulam stability, <inline-formula> <math display="inline"> <semantics> <mi>&#946;</mi> </semantics> </math> </inline-formula>&#8315;Hyers&#8315;Ulam stability and <inline-formula> <math display="inline"> <semantics> <mi>&#946;</mi> </semantics> </math> </inline-formula>&#8315;Hyers&#8315;Ulam&#8315;Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Gr&#246;nwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.