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

In this paper, we study the critical -Laplacian equation of Kirchhoff type -(integral |del|) Delta + ( )||(-2) = ()()+||*(-2), is an element of , where is the Kirchhoff function, Delta = div(|del|(-2)del) with /2 < < and >= 2, >0 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.