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ON THE SINGULAR VARIATIONAL PROBLEMS

谭经刚、杨健夫

2004Acta Scientiarum Naturalium Universitatis SunyatseniMathematics被引 0

摘要

The authors deal with the singular variational problem S(a,b,λ0):=infu∈E,u(≡／)0 ∫RN(||X|-a(△)u|m+∫|x|-(a+1)m|u|m)dx/(∫RN||X|-bU|P dx)m/p as well as (S)=(S)(a,b,λ1,λ2):=u,ν,E∈,u(u,ν)(≡／)(1,1) ∫RN J(u,ν)dx/(∫RN|x|-bp|u|α|ν|βdx)m/p, whereJ(u, v) = ||x|- au|m + λ1|x|- (a+1)m|u|m + ||x|- av|m + λ2|x|- (a+1)m|v|m,N ≥ m+ 1 ＞ 2, 0 ≤ a ＜ N-m/m, a ≤ b ＜ a+ 1 and p = p(a,b) = α+β =Nm/N-m+m(b-a), α, β≥ 1, E = D1,mα(RN). The aim of this paper is to show the existence of minimizer for S(a, b, A0) and S(a, b, λ1, λ2).

引用本文（GB/T 7714）