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The Scientific World Journal
Volume 2014 (2014), Article ID 194310, 5 pages
http://dx.doi.org/10.1155/2014/194310
Research Article

Infinitely Many Weak Solutions of the -Laplacian Equation with Nonlinear Boundary Conditions

1Xingyi Normal University for Nationalities, Xingyi, Guizhou 562400, China
2Human Resources and Social Security Bureau, Buyi and Miao Autonomous Prefecture in Southwest Guizhou, Guizhou 562400, China

Received 24 August 2013; Accepted 27 October 2013; Published 14 January 2014

Academic Editors: E. A. Abdel-Salam and P. Candito

Copyright © 2014 Feng-Yun Lu and Gui-Qian Deng. 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.

Abstract

We study the following -Laplacian equation with nonlinear boundary conditions: and where is a bounded domain in with smooth boundary . We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and do not need to satisfy the or condition.