Sign‐changing solution to a critical p‐Kirchhoff equation with potential vanishing at infinity in ℝN

In this paper, we study the critical p$$ p $$‐Laplacian equation of Kirchhoff type −M∫ℝN|∇u|pdxΔpu+V(x)|u|p−2u=λK(x)f(u)+|u|p∗−2u,x∈ℝN,$$ -M\left({\int}_{{\mathrm{\mathbb{R}}}^N}{\left|\nabla u\right|}^p dx\right){\Delta}_pu+V(x){\left|u\right|}^{p-2}u=\lambda K(x)f(u)+{\left|u\right|}^{p^{\ast }-2}u,x\in {\mathrm{\mathbb{R}}}^N, $$ where M$$ M $$ is the Kirchhoff function, Δpu=div(|∇u|p−2∇u)$$ {\Delta}_pu=\operatorname{div}\left({\left|\nabla u\right|}^{p-2}\nabla u\right) $$ with N2