Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1323-1332.

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A p-Laplace Eigenvalue Problem with Coercive Potentials

Jingran He(),Helin Guo(),Wenqing Wang*   

  1. Center of Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070
  • Received:2020-10-14 Online:2021-10-26 Published:2021-10-08
  • Contact: Wenqing Wang;
  • Supported by:
    the NSFC(11931012);the NSFC(11871387)


In this paper, we are concerned with the asymptotic behavior of solutions for a p-Laplace eigenvalue problem with coercive potentials. The bottom of the potential (The set of global minimum points of the potential) is an ellipsoid, we prove that the solutions of the problem will blow up at one of the endpoints of the major axis of the ellipsoid as the related parameter tends to a threshold value, and we also give the exact blow-up rate.

Key words: p-Laplace, Eigenvalue problem, Asymptotical behavior, Blow-up rate

CLC Number: 

  • O175.2