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
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.