A Bifurcation-Type Result for Nonlinear Neumann Eigenvalue Problems

Abstract

We consider a nonlinear Neumann eigenvalue problem driven by the p-Laplacian and with a (p – 1)-sublinear reaction. Using variational methods together with suitable truncation techniques, we prove a bifurcation-type theorem for the eigenvalue problem. Namely, we show that there is a critical parameter value λ_* > 0 such that for all λ > λ_* the problem has at least two positive solutions, for λ = λ_* there is at least one positive solution and for λ ∈ (0, λ_*) no positive solutions exist.