Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in [formula omitted].

In this paper, we first prove the uniqueness of positive ground state solution for the following Kirchhoff equation in R 3 with constant coefficients { − ( a + b ∫ R 3 | ∇ u | 2 ) Δ u + c u = d | u | p − 1 u in R 3 , u > 0 , u ∈ H 1 ( R 3 ) , where a , b , c , d > 0 are positive constants, 3 < p < 5 . Then we use the uniqueness result to obtain the existence and concentration theorems of positive ground state solutions to the following Kirchhoff equation with competing potential functions − ( ε 2 a + ε b ∫ R 3 | ∇ u | 2 ) Δ u + V ( x ) u = K ( x ) | u | p − 1 u in R 3 , for a sufficiently small positive parameter ε . [ABSTRACT FROM AUTHOR]