Exact number of solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian ✩

In this paper, exact number of solutions are obtained for the one-dimensional p-Laplacian in a class of two-point boundary value problems. The interesting point is that the nonlinearity f is general form: f (u) = λg(u) + h(u). Meanwhile, some properties of the solutions are given in details. The arguments are based upon a quadrature method. © 2007 Elsevier Inc. All rights reserved.