A result on a class of elliptic equations involving Kirchhoff type nonlocal term. (15th January 2017)

• Record Type: Journal Article
• Authors: Liu, Jiu; Yan, Zhongquan; Zheng, Zhibo
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 2(2017)
• Page Start: 355
• Page End: 361
• Publication Date: 2017-01-15
• Subjects: Elliptic equations -- Kirchhoff type nonlocal term -- Variational method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.11.036
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In the paper, we consider the following elliptic equations involving Kirchhoff type nonlocal term (0.1) − ( a + b ∫ R 3 | ∇ u | 2 d x ) △ u + V ( x ) u = f ( u ), x ∈ R 3, in which a ≥ 0, b > 0, the nonlinear term f satisfies the Berestycki–Lions conditions. Under some assumptions on V, we obtained equation Eq.(0.1) has at least a solution.