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Existence of Positive Ground State Solutions for Choquard Systems

Authors
  • Deng, Yinbin1
  • Jin, Qingfei2
  • Shuai, Wei1
  • 1 Central China Normal University, Hubei Key Laboratory of Mathematical Sciences, 430079 , (China)
  • 2 Jianghan University, 430056 , (China)
Type
Published Article
Journal
Advanced Nonlinear Studies
Publisher
De Gruyter
Publication Date
Jul 16, 2020
Volume
20
Issue
4
Pages
819–831
Identifiers
DOI: 10.1515/ans-2020-2099
Source
De Gruyter
Keywords
License
Yellow

Abstract

We study the existence of positive ground state solution for Choquard systems. In the autonomous case, we prove the existence of at least one positive ground state solution by the Pohozaev manifold method and symmetric-decreasing rearrangement arguments. Moreover, we show that each positive ground state solution is radial symmetric. While, in the nonautonomous case, a positive ground state solution is obtained by using a monotonicity trick and a global compactness lemma. We remark that, under our assumptions of the nonlinearity Wu{W_{u}}, the search of ground state solutions cannot be reduced to the study of critical points of a functional restricted to a Nehari manifold.

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