In this paper, we study the planar Schrodinger–Newton system with a Coulomb potential where the nonlinearity is super-linear at zero and exponential critical at infinity. With a weaker condition than the Nehari type monotonic condition, we obtain a least-energy sign-changing solution via the variational method. Moreover, we obtain the existence of ground states, and the energy of any nodal solution is strictly larger than two times the least energy. We also give some convergence properties of the ground states.

中文翻译：

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具有指数临界增长的平面薛定谔-牛顿系统的符号变化解和基态

在本文中，我们研究了具有库仑势的平面薛定谔-牛顿系统，其中非线性在零处为超线性，在无穷大处为指数临界。在比 Nehari 型单调条件更弱的条件下，我们通过变分方法获得了最小能量符号变化的解决方案。而且，我们得到基态的存在性，任何节点解的能量都严格大于最小能量的两倍。我们还给出了基态的一些收敛特性。