Multiplicity of Nontrivial Solutions for Kirchhoff Type Problems. (22nd December 2010)

• Record Type: Journal Article
• Authors: Cheng Cheng, Bitao Bitao; Wu Wu, Xian Xian; Liu Liu, Jun Jun
• Other Names: Zhang Zhang Zhitao Zhitao Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-12-22
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/268946
• Languages: English
• ISSNs: 1687-2762

Abstract

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.