Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1899-1910.doi: 10.1016/S0252-9602(11)60369-X

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INFINITELY MANY SOLUTIONS FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS

 LI Ke, WEI Hong-Jun   

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2009-12-14 Revised:2010-09-08 Online:2011-09-20 Published:2011-09-20
  • Supported by:

    The work is supported by Natural Science Foundation of China (10971199) and Natural Science Foundations of Henan Province (092300410067).

Abstract:

Let X = (X1,  … , Xm) be an infinitely degenerate system of vector fields. The aim of this paper is to study the existence of infinitely many solutions for the sum of operators ΔX =∑mj=1X*j Xj .

Key words: degenerate elliptic equations, logarithmic Sobolev inequality

CLC Number: 

  • 35J60
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