The existence of nontrivial solutions for the critical Kirchhoff type problem in RN. (15th December 2017)

• Record Type: Journal Article
• Authors: Zhang, Jian; Ji, Yanju
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 12(2017)
• Page Start: 3080
• Page End: 3094
• Publication Date: 2017-12-15
• Subjects: Kirchhoff type problem -- Critical growth -- Variational method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.08.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we study the problem (0.1) − a + b ∫ R N | ∇ u | 2 d x Δ u + V ( x ) u = μ f ( u ) + g ( x ) u 2 ∗ − 1 in R N, where N ≥ 3, a, b > 0 . When N = 3 and μ > 0 is small, under suitable conditions on V, f and g, we prove(0.1) has two nontrivial solutions. When N ≥ 4 and g ( x ) = 1, we also obtain the existence and non-existence results.