Existence of solution for an impulsive differential system with improved boundary value conditions

Abstract

In this paper, we study the existence of solution for a class of impulsive integro-differential equations. Different from traditional periodic and anti-periodic boundary value problems, a more general boundary condition introduced in this new system. First, we obtain some new comparison principles. Then, we obtain the expression of the solution for a class of linearized systems. Finally, the existence of extremal solutions for the new boundary value system are obtained by using the monotone iterative technique. The theoretical results obtained have wider applications in practical fields.

Keywords

• boundary value problem
• integro-differential equation
• extremal solutions
• monotone iterative technique