一类奇异临界椭圆方程组的极小能量解

Least Energy Solutions for a Class of Singular Critical Elliptic Systems

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摘要研究一类含Sobolev临界指数与非线性耦合项的奇异椭圆方程组,应用变分方法,通过Nehari流形和集中紧性原理证明对应的能量泛函满足局部的(PS)_c条件,得到了这类方程组极小能量解的存在性. In this paper,a class of singular elliptic systems involving Sobolev critical exponents and coupled nonlinear terms are studied.By using Nehari manifold and concentrationcompactness principle,the existence results of least energy solutions are obtained by proving that the energy functional corresponding to the systems satisfies the（PS）_C condition.

作者吕登峰

机构地区湖北工程学院数学与统计学院

出处《数学物理学报（A辑）》 CSCD 北大核心 2012年第6期1136-1148,共13页 Acta Mathematica Scientia

基金湖北省教育厅科研计划重点项目(D20122605) 湖北工程学院自然科学项目(Z2012003)资助

关键词椭圆方程组临界指数 NEHARI流形集中紧性原理极小能量解 Elliptic system Critical exponent Nehari manifold Concentration-compactness principle Least energy solution

分类号 O175.25 [理学—基础数学]

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数学物理学报（A辑）

2012年第6期

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一类奇异临界椭圆方程组的极小能量解

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