Journal of the
Korean Mathematical Society JKMS

In this paper, we study the existence of infinitely many large energy solutions for the supercubic fractional Schr\"{o}dinger-Poisson systems. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-know Ambrosetti-Rabinowitz type condition. We obtain three different existence results in this setting by using the Fountain Theorem, all these results extend some results for semelinear Schr\"{o}dinger-Poisson systems to the nonlocal fractional setting.

Keywords: Fractional Schr\"{o}dinger-Poisson system, variational method, fountain theorem

MSC numbers: Primary 35Q40, 35J50, 58E05

Supported by: This work was financially supported by Innovation Fund Project for Graduate Students of Yunnan Normal University, Natural Science Foundation of Heilongjiang Province (JJ2016ZR0019) and Natural Science Foundation of China (11771385, 11661083).