EXISTENCE AND EXPONENTIAL STABILITY FOR A NEW CLASS OF FIRST-ORDER IMPULSIVE EVOLUTION EQUATIONS

The aim of this paper is to present systematic methods for analyzing the existence and the exponential stability of a new class of first-order impulsive evolution equations. We initially provide two existence results of mild solutions for the equations using two kinds of methods. Subsequently, we also explore the exponential stability of the equation. Lastly, we present some applications in differential hemivariational inequalities to demonstrate our main results.