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引用次数: 0
摘要
在本文中，我们建立了一类非线性分式薛定谔-泊松系统的驻波解的存在性，该系统涉及具有亚临界和临界增长的非线性。我们假设势 V 满足 Palais-Smale 类型条件，或者存在一个有界域 \(\varOmega \)，使得 V 在 \(\partial \varOmega \)中没有临界点。为了克服问题的 "不紧凑性"，我们将 Del Pino-Felmer 的惩罚技术与 Moser 的迭代法以及 Alves [1] 的一些观点结合起来。
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases
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].
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