Existence of positive solutions to some impulsive second-order integrodifferential equations

Abstract

In this article, we consider an initial-value problem for second-order nonlinear integrodifferential equations with impulses in a Banach space. By using the monotone iterative technique in a cone together with Arzela-Ascoli theorem and the dominated convergence theorem, we establish the existence of positive solutions of such a problem.

Keywords

• Integrodifferential equation
• impulses
• positive solution
• cone theory
• Arzela-Ascoli theorem