In this paper we study a quasilinear elliptic system coupled by a Schrödinger equation with p-Laplacian operator and a Poisson equation. Some scaling transformation and ingenious methods are applied to produce the bounded Palais-Smale sequences and the existence of nontrivial solutions for the system is obtained by the mountain pass theorem.

中文翻译：

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关于拟线性薛定谔-泊松系统

在本文中，我们研究了由薛定谔方程与p -拉普拉斯算子和泊松方程耦合的拟线性椭圆系统。应用一些标度变换和巧妙的方法来产生有界Palais-Smale序列，并且通过山口定理获得系统的非平凡解的存在性。