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 (ϕ(x )) + λf(t,x,x ) = 0 in (0, 1), x(0) = x(1) = 0, where ϕ(x) = |x|p−2x, p >1, λ>0.  2003 Elsevier Inc. All rights reserved