收稿日期: 2010-10-09
修回日期: 2010-11-08
网络出版日期: 2011-09-15
基金资助
Supported by the Presidential Foundation of GUCAS
Some remarks on a quasilinear elliptic equation with critical exponent
Received date: 2010-10-09
Revised date: 2010-11-08
Online published: 2011-09-15
研究了如下的拟线性椭圆型方程:
其中, Ω是RN 中具有光滑边界的有界区域,Δpu=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.
关键词： 拟线性椭圆型方程; 临界指数; Ekeland变分原理; 参数计算
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]. 中国科学院大学学报, 2011 , 28(5) : 583 -590 . DOI: 10.7523/j.issn.2095-6134.2011.5.003
We investigate the following quasilinear elliptic equation:
where Ω is a bounded domain in RN with smooth boundary, Δpu=div(| ▽ 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 (1λ), which can be explicitly calculated.
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