Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results - Drábek, Pavel (Topological Methods in Nonlinear Analysis, 2005)
In this paper we address the existence and multiplicity results for -Δ_p u -λ |u|^p-2 u = h (x,u) &in Ω, u = 0 &on Ω, where p> 1, Δ_p u = div(| abla u|^p-2 abla u), h is a bounded function and the spectral parameter λ stays ``near’’ the principal eigenvalue of the p-Laplacian. We show how the bifurcation theory combined with certain asymptotic estimates yield desired results.