The fractional Schr\"{o}dinger-Poisson systems with infinitely many solutions
J. Korean Math. Soc. 2020 Vol. 57, No. 2, 489-506
https://doi.org/10.4134/JKMS.j190156
Published online March 1, 2020
Tiankun Jin, Zhipeng Yang
Daqing Normal University; Yunnan Normal University
Abstract : 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
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