Boundary Value Problems
Volume 2008 (2008), Article ID 403761, 12 pages
doi:10.1155/2008/403761
Multiple nodal solutions for some fourth-order boundary value problems via admissible invariant sets
Yang Yang1
, Jihui Zhang1
and Zhitao Zhang3
1Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097, China
3Academy of Mathematics and System Sciences, Institute of Mathematics, the Chinese Academy of Sciences, Beijing 100080, China
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.