Existence of sign-changing solutions for Kirchhoff equations with critical or supercritical nonlinearity

Abstract In this paper, we consider the following Kirchhoff equation − a + b ∫ R 3 | ∇ u | 2 d x Δ u + V ( x ) u = f ( u ) + λ | u | p − 2 u , in R 3 , where a , b > 0 are constants, λ > 0 is a real parameter, p ≥ 6 and V , f satisfy suitable conditions. By using a truncation argument, we prove that the existence of a sign-changing solution for this equation. Our results can be regarded as the complementary work of Li et al. (2017) and Li and Geng (2019).