Abstract

In this paper we will use the degree theory to give an existence result to the boundary value problem of nonlinear perturbations of the scalar p-Laplacian with the multi-point boundary condition involving the Lebesgue-Stieltjes integral. Among the boundary conditions considered in this paper, we will find also the optimal bounds on the growth of the nonlinear perturbations in our existence result. © 2004 Elsevier Ltd. All rights reserved.