Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

Abstract

In this paper we present existence results for solutions of nonlinear second-order boundary value problems with impulses. Our impulses are applied at p points in the interval and given implicitly by nonlinear functions of the solution. Moreover we allow functional dependence on the solution. Our existence results follow from the existence of a pair of well ordered lower and upper solutions. We generalize earlier results of Cabada and Tomec˘ek, allowing more general compatible boundary conditions, impulses and φ -Laplacian equations.