Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (3): 493-499.

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Morse Indices and Liouville Type Theorems for Weighted Elliptic Equations

Xiao Yingying, Zheng Xiongjun   

  1. Department of Mathematics, Jiangxi Normal University, Nanchang 330022
  • Received:2015-10-11 Revised:2016-03-23 Online:2016-06-26 Published:2016-06-26
  • Supported by:

    Supported by the NSFC (11271170) and Gan-Po Talent 555 Project of Jiangxi Province

Abstract:

This paper is concerned with Liouville type theorems for weighted semilinear elliptic equations
u=|x|α|u|p-1u,x∈RN
and
u=|x|α|u|p-1u,x∈R+N,u|∂R+N=0,
where N ≥ 3 and α>-2. We prove that the bounded solutions of the above problems with finite Morse indices are zero when 1 < p < (N+2α+2)/(N-2).

Key words: Morse indices, Liouville type theorems

CLC Number: 

  • O175.25
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