Sign-changing solution for a logarithmic Kirchhoff type problem

This paper is devoted to study the following logarithmic Kirchhoff problem ( a + b ∫ R 3 ( | ∇ u | 2 + V ( x ) u 2 ) d x ) ( − Δ u + V ( x ) u ) = | u | p − 2 u log ⁡ | u | , where a , b > 0 , 2 p 4 . Under some assumptions on the potential function V ( x ) , we prove the existence of a sign-changing solution to this problem for b > 0 small enough by using the truncated technique and constraint variational method.