Boundary Value Problems 
Volume 2008 (2008), Article ID 403761, 12 pages
doi:10.1155/2008/403761
Research Article

Multiple Nodal Solutions for Some Fourth-Order Boundary Value Problems via Admissible Invariant Sets

Yang Yang,1,2 Jihui Zhang,1 and Zhitao Zhang3

 1Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097, China
2School of Science, Jiangnan University, Wuxi 214122, China
3Academy of Mathematics and System Sciences, Institute of Mathematics, the Chinese Academy of Sciences, Beijing 100080, China
Received 6 May 2008; Accepted 16 September 2008

Recommended by Donal O'Regan

Abstract

Existence and multiplicity results for nodal solutions are obtained for the fourth-order boundary value problem (BVP) u(4)(t)=f(t,u(t)), 0<t<1, u(0)=u(1)=u′′(0)=u′′(1)=0, where f:[0,1]×R→R is continuous. The critical point theory and admissible invariant sets are employed to discuss this problem.