International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 9, Pages 575-586
doi:10.1155/S0161171203006744

The eigenvalue problem for the p-Laplacian-like equations

Zu-Chi Chen and Tao Luo

 Department of Mathematics, University of Science and Technology of China, Anhui, Hefei 230026, China
Received 16 February 2001

Abstract

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.