| Rn上一类拟线性椭圆方程正解的存在性 |
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| 引用本文： | 胡业新. Rn上一类拟线性椭圆方程正解的存在性[J]. 应用数学, 2003, 16(4): 84-88 |
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| 作者姓名： | 胡业新 |
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| 作者单位： | 上海交通大学数学系,上海,200240 |
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| 基金项目： | SupportedbyNNSFofChina (10271077)andbytheNationalEducationalCommittee’sDoctorprogramFundsofChina ( 970 2 4 811) . |
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| 摘 要： | 本文讨论了Rn 上如下一类带临界增长的拟线性椭圆方程正解的存在性 :-div(｜ u｜p- 2 u) -axn｜ u｜p- 2 u xn +｜u｜p- 2u=up - 1 ,xn ≠ 0 ,x∈Rn.这里 ,1
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| 关 键 词： | 拟线性椭圆方程 正解 存在性 临界增长 集中列紧原理 Sobolev空间 |
On the Existence of Positive Solution for a Class of Elliptic Equations in Rn |
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| HU Yexin. On the Existence of Positive Solution for a Class of Elliptic Equations in Rn[J]. Mathematica Applicata, 2003, 16(4): 84-88 |
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| Authors: | HU Yexin |
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| Abstract: | In this paper,the existence of positive solution for a class of quasilinear elliptic equationsinvolving Sobolev critical exponent:-div(|(△) u|p-2(△) u)-a/xn|(△)u | p-2(e)u/(e)xn+up-1=up*-1,xn≠0,x∈Rn. was discussed in Rn,where 1＜p＜n,0＜a＜p-1,p* =(n+a)p/n+a-p is the Sobolev crit-ical exponent W1,p (a, Rn) → Lq (a,Rn), the embedding is not compact. By using the Lions' concen-tration compactness principle after revised,we proved this problem has at least a positive solution. |
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| Keywords: | Weighted sobolev space Quasilinear elliptic equation So bolev critical exponent Positive solution |
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