Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (5): 895-901.

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Generalized Picone's Identity and Its Applications for Heisenberg-Greiner Operators

Wang Shengjun1, Han Yazhou2   

  1. 1. Department of Mathematics, Qinghai Normal University, Xining 810008;
    2. Department of Mathematics, College of Science, China Jiliang University, Hangzhou 310018
  • Received:2016-11-13 Revised:2017-04-16 Online:2017-10-26 Published:2017-10-26
  • Supported by:
    Supported by the NSFC (11201443)

Abstract: In this paper, a generalized version of the Picone's identity is established for Heisenberg-Greiner operators. As applications, Hardy type inequality, Sturmian Comparison principle and strict monotonicity of the principal eigenvalue are given. Finally, quasilinear system with singular nonlinearity also is studied.

Key words: Heisenberg-Greiner operators, Picone's identity, Hardy type inequality, Sturmian comparison principle, Strict monotonicity of the principal eigenvalue

CLC Number: 

  • O175.2
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