Sentence examples for impulsive evolution from inspiring English sources

Since the end of last century, impulsive evolution equations and impulsive optimal controls have attracted much attention because many evolutional processes are subject to abrupt changes in the form of impulses (see [1 11]).

The impulsive evolution operator has the following properties.

The operator is called impulsive evolution operator associated with and.

This paper is concerned with controlled nonlinear impulsive evolution equations with nonlocal conditions.

This paper deals with the periodic boundary value problems for nonlinear impulsive evolution equations with controls.

In this paper, we study periodic BVPs for fractional order impulsive evolution equations.

In Section 2, the properties of the impulsive evolution operator are collected.

Thus, the impulsive evolution equation (3.5) has a unique strong T-periodic solution.

Next, four sufficient conditions that guarantee the exponential stability of impulsive evolution operator are given.

For the impulsive evolution equation (3.5), we have the following theorem.

Let (x_{1}), (x_{2}) be strong T-periodic solutions of the impulsive evolution equation (3.5).