In this work, we are concerned with the existence and nonexistence of ground state solutions for the following class of quasilinear Schrodinger coupled systems taking into account periodic or asymptotically periodic potentials. The nonlinear terms are superlinear at infinity and at the origin. By using a change of variable, we turn the quasilinear system into a nonlinear system where we can establish a variational approach with a fine analysis on the Nehari method. For the nonexistence result, we compare the potentials with periodic potentials proving the nonexistence of ground state solutions.

中文翻译：

---

周期和渐近周期拟线性椭圆系统

在这项工作中，我们关注以下类拟线性薛定谔耦合系统的基态解的存在和不存在，同时考虑了周期性或渐近周期性势。非线性项在无穷远和原点处是超线性的。通过使用变量的变化，我们将拟线性系统转变为非线性系统，在那里我们可以建立一种对 Nehari 方法进行精细分析的变分方法。对于不存在的结果，我们将电位与证明基态解不存在的周期性电位进行比较。