| 一个含临界指数的拟线性椭圆型方程的注记 |
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| 引用本文： | 刘星,孙义静.一个含临界指数的拟线性椭圆型方程的注记[J].中国科学院研究生院学报,2011,28(5). |
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| 作者姓名： | 刘星 孙义静 |
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| 作者单位： | 中国科学院研究生院数学科学学院,北京,100049 |
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| 基金项目： | Supported by the Presidential Foundation of GUCAS |
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| 摘 要： | 研究了如下的拟线性椭圆型方程:△pu+uq+λup*-1=0,u∈W1o,p(Ω), (1λ)其中,Ω2是RN中具有光滑边界的有界区域,△pu=div( |▽u|p-2▽u),N≥3,2≤p＜N,0＜q＜1,p*=NP/N-P.设λ*(Ω,p,q)是拟线性椭圆型方程(1λ)可解的参数集的上确界.运用变分方法,在不要求具有对称性质的一般区域Ω上得到了λ*(Ω,p,q)的一个可以精确计算的下界.
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| 关 键 词： | 拟线性椭圆型方程 临界指数 Ekeland变分原理 参数计算 |
Some remarks on a quasilinear elliptic equation with critical exponent* |
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| LIU Xing,SUN Yi-Jing.Some remarks on a quasilinear elliptic equation with critical exponent*[J].Journal of the Graduate School of the Chinese Academy of Sciences,2011,28(5). |
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| Authors: | LIU Xing SUN Yi-Jing |
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| Institution: | LIU Xing,SUN Yi-Jing(School of Mathematics,Graduate University,Chinese Academy of Sciences,Beijing 100049,China) |
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| Abstract: | We investigate the following quasilinear elliptic equation:△p u + uq + λup*-1 =0,u ∈ W1o,p(Ω),(1λ)where Ω is a bounded domain in RN with smooth boundary,△pu =div(| V▽u| p-2▽u),N ≥ 3,2 ≤ p＜ N,0 ＜ q ＜ 1,and p* =NP/N-p.By using variational methods,we obtain a lower bound of the extremal value λ* (Ω,p,q) for equation (1 λ ),which can be explicitly calculated. |
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| Keywords: | quasilinear elliptic equation critical exponent Ekeland' s variational principle extremal value |
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