Ground state solutions for asymptotically periodic coupled Kirchhoff‐type systems with critical growth

In this paper, we consider the coupled system of Kirchhoff‐type equations:− a + b ∫R 3| ∇ u | 2Δ u + V ( x ) u = λ F u ( x , u , v ) + | u | τ − 2 u ,in R 3 ,− c + d ∫R 3| ∇ v | 2Δ 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.