On an eigenvalue problem involving the one-dimensional p-Laplacian

We apply general results on operator equations in ordered spaces and properties of the principal eigenvalues for weighted semi-linear equations to prove the existence of a global continua of positive solutions and eigenvalue intervals to the problem (phi(x'))'+lambdaf (t, x, x')=0 in (0, 1), x(0)=x(1)=0, where phi (x)=\x\(p-2)x, p>1, lambda>0. (C) 2003 Elsevier Inc. All rights reserved.