JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 74-78.doi: 10.6040/j.issn.1671-9352.0.2018.638

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Existence of nontrival solutions for a class of Schrödinger-Poisson systems

CHEN Li-zhen1, FENG Xiao-jing2, LI Gang3   

  1. 1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China;
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China;
    3. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Published:2019-10-12

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Abstract: We investigate a class of Schrödinger-Poisson systems, by means of variational method and critical point theory. Here, the Poisson term is a more general form. By adding quasi-critical growth and AR conditions to the nonlinear term, we prove the existence of nontrival solution of the system. The result supplement and promote the previous resluts on the Schrödinger-Poisson systems.

Key words: Schrö, dinger-Poisson system, variational method, mountain pass theorem

CLC Number: 

  • O176.3
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