Sign-changing solutions for the stationary Kirchhoff problems involving the fractional Laplacian in [formula omitted

Abstract

In this paper, we study the existence of least energy sign-changing solutions for a Kirchhoff-type problem involving the fractional Laplacian operator. By using the constraint variation method and quantitative deformation lemma, we obtain a least energy nodal solution ub for the given problem. Moreover, we show that the energy of ub is strictly larger than twice the ground state energy. We also give a convergence property of ub as b ↘ 0, where b is regarded as a positive parameter.