Abstract

We consider the eigenvalue problem for the following p-Laplacian-like equation: div(a(|Du|p)|Du|p2Du)=λf(x,u) in Ω, u=0 on Ω, where Ωn is a bounded smooth domain. When λ is small enough, a multiplicity result for eigenfunctions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for applications of the theorems.