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

In this paper, we consider the following quasilinear Kirchhoff-Schrodinger-Poisson system: {-(a + b integral(R3) vertical bar del u vertical bar(2) dx) Delta u +V(x)u - 1/2u Delta(u(2)) + phi u = g(u), x is an element of R-3, -Delta phi = u(2), x is an element of R-3, where a, b are positive constants, V(x) 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 u(0) 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.