The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method

Abstract

This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger-Poisson systems. There are some technical difficulties in applying variational methods directly to the problem because the quasilinear term makes it impossible to find a suitable space in which the corresponding functional possesses both smoothness and compactness properties. In order to overcome the difficulties caused by nonlocal term and quasi-linear term, we shall apply the perturbation method by adding a 4-Laplacian operator to consider the perturbation problem. And then, by using the approximation technique, a sign-changing solution with precisely two nodal domains is derived. MSC: 35J20; 35J60

Quasilinear asymptotically periodic Schrödinger–Poisson system with subcritical growth

“…So our discussion is worth considering and has an excellent prospect; this paper is also an innovation of the pioneering work. When K(x) = 1 in system (1.1), the authors in [8] took into account the systems by applying the perturbation method, and hence the existence of a sign-changing solution with precisely two nodal domains was derived. The authors in [15] studied the existence and asymptotic behavior of ground state in the whole space R 3 for the quasilinear Schrödinger-Poisson system with asymptotically linear f (t) with respect to t at infinity; see also [28] for more related results.…”

Existence and asymptotical behavior of positive solutions for the Schrödinger-Poisson system with double quasi-linear terms

“…With the help of the method of invariant sets of descending flow introduced in [30], Liu, Wang and Zhang [31] proved (4) possesses the infinitely many sign-changing solutions. For more existing results of this system, readers can refer to ( [2,5,12,13,14,18,19,23,27,36,37,38]) and the references therein.…”