The sign-changing solutions for a class of p-Laplacian Kirchhoff type problem in bounded domains

In this paper, we study the existence of sign-changing ground state solutions and properties of such solutions for a class of p-Laplacian Kirchhoff type problem. Since the appearance of the p-Laplacian Kirchhoff term, the problem becomes more complex than Kirchhoff type problem. For the purpose of overcoming the difficulty, we use a quantitative deformation lemma, degree theory, Non-Nehari manifold method and some mathematical skills to obtain a ground state sign-changing solution ub and prove that its energy is strictly larger than twice that of the ground state solutions of Nehari-type. Moreover, we also obtain the convergence property of ub as the parameter b↘0.