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

Abstract

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 solution of 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.