Boundary Value Problems
Volume 2010 (2010), Article ID 728101, 17 pages
doi:10.1155/2010/728101
Research Article

Nontrivial Solutions of the Asymmetric Beam System with Jumping Nonlinear Terms

Tacksun Jung1 and Q-Heung Choi2

1Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea
2Department of Mathematics Education, Inha University, Incheon 402-751, Republic of Korea

Received 8 October 2009; Revised 24 July 2010; Accepted 11 September 2010

Academic Editor: Raul F. Manasevich

Copyright © 2010 Tacksun Jung and Q-Heung Choi. 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 investigate the existence of multiple nontrivial solutions (ξ,η) for perturbations b1[(u+2)+-2]and b2[(u+3)+-3] of the beam system with Dirichlet boundary condition Lξ=b1[(ξ+3η+2)+-2] in (-π/2,π/2)×ℝ, Lη=b2[(ξ+3η+3)+-3] in (-π/2,π/2)×ℝ, where u+=  max  {u,0}, and μ,ν are nonzero constants. Here L is the beam operator in ℝ2 , and the nonlinearity (b1[(u+2)+-2]+b2[(u+3)+-3] crosses the eigenvalues of the beam operator.