Boundary Value Problems
Volume 2010 (2010), Article ID 268946, 13 pages
doi:10.1155/2010/268946
Research Article

Multiplicity of Nontrivial Solutions for Kirchhoff Type Problems

Bitao Cheng,1 Xian Wu,2 and Jun Liu1

1College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, China
2Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, China

Received 25 October 2010; Accepted 14 December 2010

Academic Editor: Zhitao Zhang

Copyright © 2010 Bitao Cheng et al. 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

By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems ∫ − ( 𝑎 + 𝑏 Ω | ∇ 𝑢 | 2 ) Δ 𝑢 = 𝑓 ( 𝑥 , 𝑢 ) , in Ω ; 𝑢 = 0 , on 𝜕 Ω . Existence results of two nontrivial solutions and infinite many solutions are obtained.