Existence and multiplicity of sign-changing solutions for quasilinear Schrödinger-Poisson system

In this paper, we consider the quasilinear Schr & ouml;dinger-Poisson system {-Delta u + V(x)u + phi u - [Delta(1 + u(2))(1/2)]u/2(1 + u(2))(1/2 )= f(u) in R-3, -Delta phi = u(2 )in R-3, where V is a given coercive potential and the nonlinearity includes pure power type such as f(u) = |u|(p-2)u with p > 8 - 2 root 6. Firstly, we study the case of p > 4, and prove existence and multiplicity of sign-changing solutions through the method of invariant sets of descending flow. Then we study the case of 8 - 2 root 6 < p <= 4 and obtain a similar result by making use of the perturbation method.