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含临界耦合非线性项的奇异椭圆方程组的非平凡解

Nontrivial Solutions for Singular Elliptic Systems Involving Critical Coupling Nonlinear Terms
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摘要 研究了有界区域上一类含Sobolev临界指数与奇异位势的带权椭圆方程组,通过Caffarelli-Kohn-Nirenberg不等式与精确的能量估计,并运用山路引理得到了这类方程组非平凡解的存在性. This paper deals with a class of weighted nonlinear elliptic systems involving Sobolev critical exponents and singular potentials in bounded domains.By using the Caffarelli-Kohn-Nirenberg inequality and delicate energy estimates,the existence of their nontrivial solutions is obtained by exploiting the mountain pass theorem.
作者 徐国进 吕登峰
机构地区 湖北工程学院数学与统计学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第8期104-107,共4页 Journal of Southwest University(Natural Science Edition)
基金 湖北省教育厅重点科研项目(D20122605) 湖北工程学院青年项目(Z2012003)
关键词 非平凡解 椭圆方程组 SOBOLEV临界指数 Caffarelli-Kohn-Nirenberg不等式 nontrivial solution elliptic system Sobolev critical exponent Caffarelli-Kohn-Nirenberg inequality
分类号 O175.25 [理学—基础数学]
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参考文献10

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二级参考文献17

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西南大学学报（自然科学版）
2012年 第8期

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