Eigenvalues and the one-dimensional p-laplacian

Abstract

We consider the boundary value problem (φp(u′))′ + λF(t,u) =0, with p > 1, t ∈(0, 1), u(0) = u(1) =0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed. © 2002 Elsevier Science (USA).