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1 Introduction and Main Results.For n≥2,we consider the following Dirichlet eigenvalue problem.{-△μu=λu,χ∈Ω;u=0,χ∈?Ω}(1.1)on a bounded open domainΩR^n,with smooth boundary?Ω,where△μis a degenerate elliptic operator generated by a system of real vector fie