Quasilinearization method for first-order impulsive integro-differential equations

Abstract

In this article we study first-order impulsive integro-differential equations with integral boundary conditions, employing the method of quasilinearization with reversed ordering upper and lower solutions. We obtain two monotone sequences of iterates converging uniformly and quadratically to the unique solution of the problem. Two examples are given to illustrate the applications of the established results.

Keywords

• Impulsive integro-differential equations
• quasilinearization
• integral boundary conditions
• quadratic convergence
• upper and lower solutions