2012一类临界指数增长的椭圆型方程组正解的存在性

江汉大学学报（自然科学版） ›› 2012, Vol. 40 ›› Issue (3): 12-14.

2012一类临界指数增长的椭圆型方程组正解的存在性

万优艳

江汉大学数学与计算机科学学院，湖北武汉430056

收稿日期:2012-04-05 出版日期:2012-06-20 发布日期:2013-11-07
作者简介:万优艳(1975—)，女，副教授，博士，研究方向:椭圆型偏微分方程。

The Existence of Positive Solution to an Elliptic System Involving Sobolev Critical Exponent

WAN You-yan

School of Mathematics and Computer Sciences,Jianghan University,Wuhan 430056,Hubei,China

Received:2012-04-05 Online:2012-06-20 Published:2013-11-07

摘要/Abstract

摘要： 研究了一类临界指数增长的椭圆型方程组。通过变分法，得到方程组的能量泛函在零点附近的局部极小值点的存在性，且该极小值点为方程组的正解。证明了当方程组的扰动项趋于零时，方程组的正解也趋于零。

关键词: 临界指数, 椭圆型方程组, 正解

Abstract: This paper studies an elliptic system involving Sobolev critical exponent. By the variational methods, we can obtain the existence of local minimum point of the energy functional related to the system which is near zero, and the local minimum point is the positive solution to this system. Moreover, It is also proved that this positive solution tends to zero when the perturbed term goes to zero.

Key words: critical exponent, elliptic system, positive solution

中图分类号:

O175.25

万优艳. 2012一类临界指数增长的椭圆型方程组正解的存在性[J]. 江汉大学学报（自然科学版）, 2012, 40(3): 12-14.

WAN You-yan. The Existence of Positive Solution to an Elliptic System Involving Sobolev Critical Exponent[J]. Journal of Jianghan University(Natural Science Edition), 2012, 40(3): 12-14.

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