Sign‐changing solution to a critical pp‐Kirchhoff equation with potential vanishing at infinity in ℝNRN

In this paper, we study the critical ‐Laplacian equation of Kirchhoff type where is the Kirchhoff function, with and is a parameter, , and the potentials and vanish at infinity. Under some suitable assumptions on , by using the constraint minimization approach, we obtain a least energy sign‐changing solution to this problem if is large enough and show the energy of is strictly larger than twice that of the ground state solutions. Moreover, by considering a wider class of and , we exploit the truncation argument to find a nontrivial solution if is sufficiently large via some analytic skills.