Infinitely many bound state solutions of Kirchhoff problem in R3. (June 2016)

• Record Type: Journal Article
• Authors: Xie, Qilin; Ma, Shiwang; Zhang, Xu
• Is Part Of: Nonlinear analysis. Volume 29(2016)
• Page Start: 80
• Page End: 97
• Publication Date: 2016-06
• Subjects: Kirchhoff type problem -- Infinitely -- Bound state solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.10.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In the present paper, we consider the following Kirchhoff problem ( K ) { − ( 1 + b ∫ R 3 | ∇ u | 2 d x ) Δ u + a ( x ) u = | u | p − 2 u, in R 3, u ∈ H 1 ( R 3 ), where b > 0 and p ∈ ( 4, 6 ) . Under some suitable decay assumptions but without any symmetry property on a ( x ), we obtain infinitely many bound state solutions of this problem.