Existence and multiplicity results for a class of p-Laplacian problems with Neumann-Robin boundary conditions

In this paper, we study the following Neumann-Robin boundary value problem [GRAPHICS] where alpha is an element of R, lambda > 0 are parameters and p > 1, and p' = p/p-1 is the conjugate exponent of p and rho(p)(x) = vertical bar x vertical bar(p-2)x for all x c R where (rho(p)(u'))' is the one dimensional p-Laplacian and f E C-2[0,infinity) such that f(0) < 0, or f(0) > 0, and also f is increasing and concave up. We shall investigate the existence and multiplicity of nonnegative solutions. Note that in this paper, we shall establish our existence results by using the quadrature method. (c) 2005 Elsevier Ltd. All rights reserved.