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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 635265, 11 pages
http://dx.doi.org/10.1155/2013/635265
Research Article

Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

1College of Science, Xi’an University of Science and Technology, Xi’an, Shaanxi 710054, China
2College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062, China

Received 5 September 2012; Accepted 22 April 2013

Academic Editor: Svatoslav Staněk

Copyright © 2013 Ying Wu and Guodong Han. 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

Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: ,   ;   , where . In particular, an infinitely many sign changing solution theorem is established. The method of the invariant set of decreasing flow is employed to discuss this problem.