拟线性Schrdinger-Poisson方程正解、负解、变号解的存在性

Existence of Signed and Sign-changing Solutions for Quasilinear Schrdinger-Poisson System

本文考虑拟线性Schrodinger-Poisson方程{-△u＋V（x）u＋Φu-1/2△（u2）u=f（x,u）,x∈R3,-△Φ=u^2,x∈R3,其中f是一个C1超线性且次临界的非线性项,V是正的有界位势.利用扰动方法,我们证明了该方程非平凡解、正解、负解、变号解的存在性.

We consider the following quasilinear SchrSdinger-Poisson system {-△u＋V（x）u＋Φu-1/2△（u2）u=f（x,u）,x∈R3,-△Φ=u^2,x∈R3 where f is C1, superlinear and subcritical nonlinearity, V is bounded positive potential By using the method of perturbation, we prove the system has non-trivial solutions positive solutions, negative solutions and sign-changing solutions.