JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 56-63.doi: 10.6040/j.issn.1671-9352.0.2020.713

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Solution to the fractional Schrödinger-Poisson systems with critical term

GUO Kai-li, FENG Xiao-jing*   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China
  • Published:2021-06-03

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Abstract: This paper studies a class of fractional Schrödinger-Poisson systems with critical term, which has recently been widely used in optimization, finance, reaction diffusion and so on. Since the problem in the system has two critical terms, it is difficult to estimate the critical value of mountain pass; and the potential function is neither periodic nor asymptotic periodic, the usual concentration-compactness method is invalid. So we employ variational method and modified concentration-compactness principle to obtain the existence of nontrivial solution of this system. This result supplements and expands on the previous results on fractional Schrödinger-Poisson systems.

Key words: fractional Schrö, dinger-Poisson system, nontrivial solution, critical exponent

CLC Number: 

  • O175.25
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