International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 575-586

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

Copyright © 2003 Zu-Chi Chen and Tao Luo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.