In this paper, we establish the existence of standing wave solutions for a class of nonlinear fractional Schrödinger-Poisson system involving nonlinearity with subcritical and critical growth. We suppose that the potential V satisfies either Palais-Smale type condition or there exists a bounded domain \(\varOmega \) such that V has no critical point in \(\partial \varOmega \). To overcome the “lack of compactness" of the problem, we combine Del Pino-Felmer’s penalization technique with Moser’s iteration method and some ideas from Alves [1].

中文翻译：

---

关于一类非线性分数阶薛定谔-泊松系统解的存在性：亚临界和临界情况

在本文中，我们建立了一类涉及亚临界和临界增长非线性的非线性分数薛定谔-泊松系统驻波解的存在性。我们假设势 V 满足 Palais-Smale 类型条件，或者存在有界域 \(\varOmega \) 使得 V 在 \(\partial \varOmega \) 中没有临界点。为了克服问题的“缺乏紧凑性”，我们将 Del Pino-Felmer 的惩罚技术与 Moser 的迭代方法以及 Alves [1] 的一些想法结合起来。