| ON THE SINGULAR VARIATIONAL PROBLEMS |
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| 引用本文： | 谭经刚,杨健夫. ON THE SINGULAR VARIATIONAL PROBLEMS[J]. 数学物理学报(B辑英文版), 2004, 24(4): 672-690 |
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| 作者姓名： | 谭经刚 杨健夫 |
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| 作者单位： | Wuhan Institute of Physics and Mathematics，Chinese Academy of Sciences，Wuhan 430071，China，Wuhan Institute of Physics and Mathematics，Chinese Academy of Sciences，Wuhan 430071，China |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 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).
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| 关 键 词： | 奇异变分问题 极小值 存在性 微分方程 |
ON THE SINGULAR VARIATIONAL PROBLEMS |
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| Tan Jinggang Yang JianfuWuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan ,China. ON THE SINGULAR VARIATIONAL PROBLEMS[J]. Acta Mathematica Scientia, 2004, 24(4): 672-690 |
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| Authors: | Tan Jinggang Yang JianfuWuhan Institute of Physics Mathematics Chinese Academy of Sciences Wuhan China |
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| Affiliation: | Tan Jinggang Yang JianfuWuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China |
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| Abstract: | |
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| Keywords: | Singular variational problem existemce of minimizer |
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