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具Hardy-Sobolev临界指数的非齐次椭圆方程的正解 被引量：1

Positive Solutions for Nonhomogeneous Elliptic Problems with Critical Hardy-Sobolev Exponents
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摘要 讨论一类具Hardy-Sobolev临界指数的非齐次半线性椭圆方程,通过应用Lions集中紧性原理建立了S_μ(Ω)的极小函数,再结合Ekeland变分原理、山路引理和Nehari流形的分析方法证明了方程在适当条件下正解的存在性与多重性. In this paper, we discuss a class of nonhomogeneous semilinear elliptic equations with critical Hardy-Sobolev exponents. We get a minimizer of Su（Ω） by using the concentration compactness principle due to Lions. Combining the Ekeland variational principle, a mountain pass lemma and the analysis methods of Nehari manifold, we prove the existence and multiplicity results of positive solutions under certain appropriate conditions.
作者 邓志颖 黄毅生
机构地区 苏州大学数学科学学院 重庆邮电大学应用数学研究所
出处 《应用数学学报》 CSCD 北大核心 2009年第6期1104-1122,共19页 Acta Mathematicae Applicatae Sinica
基金 国家自然科学基金(10571174) 江苏省高校自然科学基金(08KJB110009) 重庆邮电学院青年教师基金项目(A2005-19)资助项目
关键词 Hardy—Sobolev临界指数 正解 山路引理 集中紧性原理 critical Hardy-Sobolev exponent positive solutions mountain pass lemma concentration compactness principle
分类号 O175.25 [理学—基础数学]
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应用数学学报
2009年 第6期

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