Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (3): 510-518.

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The Existence of Minimizers for a Class of Constrained Variational Problem with Its Concentration Behavior

Gu Longjiang1, Sun Zhiyu1, Zeng Xiaoyu2   

  1. 1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071;
    2 School of Sciences, Wuhan University of Technology, Wuhan 430070
  • Received:2016-10-17 Revised:2017-03-21 Online:2017-06-26 Published:2017-06-26
  • Supported by:
    Supported by the NSFC(11471331, 11501555) and the Fundamental Research Funds for the Central University (WUT:2017IVA076)

Abstract: In this paper, we mainly discuss the existence and non-existence of minimizers for the variational functional of a p-Laplacian eigenvalue problem involving harmonic potential. Moreover, the concentration behavior of the minimizers is also investigated by using the energy method when the related parameter closes to a critical value.

Key words: Constrained variation, p-Laplacian equation, Minimizing problem, Concentration behavior

CLC Number: 

  • O175.25
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