We consider the eigenvalue problem for the following p-Laplacian-like equation: −div(a(|Du|p)|Du|p−2Du)=λf(x,u) in Ω,
u=0 on ∂Ω, where Ω⊂ℝn 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.