Multiplicity results for fourth order elliptic equations of Kirchhoff-type. Issue 5 (September 2015)

• Record Type: Journal Article
• Authors: XU, Liping; CHEN, Haibo
• Is Part Of: Acta mathematica scientia. Volume 35:Issue 5(2015)
• Page Start: 1067
• Page End: 1076
• Publication Date: 2015-09
• Subjects: fourth order elliptic equations of Kirchhoff type -- symmetric mountain pass theorem -- variational methods; 35J20 -- 35J65 -- 35J60; Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(15)30040-0
• Languages: English
• ISSNs: 0252-9602

Abstract

Abstract: In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type { Δ 2 u - ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u = f ( x, u ), x ∈ ℝ 3, u ∈ H 2 ( ℝ 3 ), where a, b > 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti-Rabinowitz type condition.