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In this paper, we consider the following quasilinear Kirchhoff–Schrödinger–Poisson system:where  a ,  b  are positive constants,is a smooth potential function and  g  is an appropriate nonlinear function. To overcome the technical difficulties caused by the quasilinear term, the perturbation method of adding 4-Laplacian operator is adapted to consider the perturbation problem, so that the corresponding functional has both smoothness and compactness in the appropriate space. Moreover, when  g  satisfies the appropriate hypotheses, a sign-changing solutionof above problem can be obtained by taking advantage of constraint variational method, the quantitative deformation lemma and approximation technique, which has precisely two nodal domains.

Sign-changing solutions for a modified quasilinear Kirchhoff–Schrödinger–Poisson system via perturbation method