On sign-changing solutions for quasilinear Schrödinger-Poisson system with critical growth

Abstract

In this paper, we consider the following quasilinear Schrödinger-Poisson system with critical growth: where , is a smooth potential function and g is a appropriate nonlinear function. For the sake of overcoming the technical difficulties caused by the quasilinear term, we shall apply the perturbation method by adding a 4-Laplacian operator to consider the perturbation problem. Moreover, when g satisfying suitable assumptions and sufficiently large μ, we take advantage of constraint variational method, the quantitative deformation lemma, Moser iteration and approximation technique to obtain a least-energy sign-changing solution , which has precisely two nodal domains.