Semi-linear impulsive higher order boundary value problems

Abstract

This paper considers two-point higher order impulsive boundary value problems, with a strongly nonlinear fully differential equation with an increasing homeomorphism. It is stressed that the impulsive effects are defined by very general functions, that can depend on the unknown function and its derivatives, till order n − 1. The arguments are based on the lower and upper solutions method, together with Leray–Schauder fixed point theorem. An application, to estimate the bending of a onesided clamped beam under some impulsive forces, is given in the last section.