On the existence of least energy solution for Kirchhoff equation in R 3

We are concerned with the following Kirchhoff‐type equation:− a + b ∫R 3| ∇ u | 2 d x Δ u +h ∞ + h ( x ) u = ( q ∞ + q ( x ) ) | u | p − 2 u inR 3 , where a , b > 0 are constants,h ∞ , q ∞ > 0 , 2 < p < 6 , and h ( x ) , q ( x ) are positive functions inC 2 ( R 3 ) satisfying h ( x ) ↘ 0 , q ( x ) ↘ 0 as | x | → ∞ . Under certain assumptions on h ( x ) , q ( x ) andh ∞ , q ∞ , we prove the existence of least energy solution for the aforementioned Kirchhoff‐type equation.