Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (4): 647-662.

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Liouville Type Theorem for an Integral System on a Half Space

Tang Sufang   

  1. School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100
  • Received:2016-10-21 Revised:2017-01-17 Online:2017-08-26 Published:2017-08-26
  • Supported by:
    Supported by the NSFC (11571268, 11572231)

Abstract: This paper considers Liouville type theorem for a system of integral equations on the upper half Euclidean space. Under the natural structure conditions, we prove the nonexistence of positive solutions to the system basing on the method of moving sphere in integral form and the Hardy-Littlewood-Sobolev (HLS) inequality.

Key words: Integral system, Liouville theorem, HLS inequality, Moving spheres method

CLC Number: 

  • O175.2
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