Ground state solutions for asymptotically periodic coupled Kirchhoff‐type systems with critical growth. (4th September 2015)

• Record Type: Journal Article
• Authors: Shi, Hongxia; Chen, Haibo
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 9(2016:Jun. 15)
• Page Start: 2193
• Page End: 2201
• Publication Date: 2015-09-04
• Subjects: asymptotically periodic -- Kirchhoff‐type equations -- critical growth -- variational methods; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3633
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider the coupled system of Kirchhoff‐type equations: − a + b ∫ R 3 | ∇ u | 2 Δ u + V ( x ) u = λ F u ( x, u, v ) + | u | τ − 2 u, in R 3, − c + d ∫ R 3 | ∇ v | 2 Δ v + V ( x ) v = λ F v ( x, u, v ) + | v | 4 v, in R 3, u, v ∈ H 1 ( R 3 ), in R 3, where 4 < τ < 6, a, c > 0, b, d ≥0 are constants and λ is a positive parameter. The main purpose of this paper is to study the existence of ground state solutions for the aforementioned system with a nonlinearity in the critical growth under some suitable assumptions on V and F . Recent results from the literature are improved and extended. Copyright © 2015 John Wiley & Sons, Ltd.