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Ground state solutions for asymptotically periodic coupled Kirchhoff‐type systems with critical growth
Author(s) -
Shi Hongxia,
Chen Haibo
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3633
Subject(s) - mathematics , ground state , nonlinear system , type (biology) , state (computer science) , constant (computer programming) , mathematical analysis , mathematical physics , physics , quantum mechanics , computer science , ecology , algorithm , biology , programming language
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.