Ground state solutions for asymptotically periodic coupled Kirchhoff‐type systems with critical growth. (4th September 2015) - Shi, Hongxia; Chen, Haibo
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.