Existence and Stability of Solutions for First Order Periodic Boundary Value Problem with Impulses

The monotone iterative technique coupled with lower and upper solutions and coincidence degree theory are powerful methods in dealing with the existence of solutions to first order nonlinear differential equations. As for stability, Lyapunov direct method has generality and very useful for studying the stability theory, but it is not convenient for constructing the Lyapunov function sometimes. In this paper, we employ iterative analysis method which is different from the above two methods to obtain both the existence and the stability of first order impulsive differential equations with periodic boundary value problem. Some new results are obtained.