International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 575-586
The eigenvalue problem for the -Laplacian-like equations
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 -Laplacian-like equation: in ,
on , where is a bounded smooth domain. When 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.