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一类带有Hardy项和Sobolev-Hardy临界指数椭圆方程的非平凡解

Existence of nontrivial solutions for a class of elliptic equations involving Hardy terms and Sobolev-Hardy critical exponents
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摘要 研究了一类带有Hardy项和Sobolev-Hardy临界指数的椭圆方程{-Δu-μ+h(x)/|x|2u=|u|2*(s)-2/|x|su+λ|u|q-2u,x∈Ω;u=0,x∈Ω{.通过运用变分方法和精确估计得到了非平凡解u∈D1,2(Ω)的存在性.其中:ΩRN(N≥3)是一个有界光滑区域,0∈Ω,λ>0,μ∈R,0≤s<2. It was discussed a class of elliptic equations involving Hardy terms and Sobolev-Hardy critical exponents {-△u-u＋h（x）/｜x｜2u=｜u｜2·（s）-2/｜x｜s u＋λ｜u｜q-2 u,x∈Ω; u=0,x∈ Ω.The existence of nontrivial solutions was proved via variational methods and delicate estimates, where Ω R N（N≥3） was an bounded domain with smooth boundary and containing the origin 0,λ〉0,u∈R,0≤s〈2.
作者 刘震 沈自飞
机构地区 浙江师范大学数理与信息工程学院
出处 《浙江师范大学学报（自然科学版）》 CAS 2013年第1期45-53,共9页 Journal of Zhejiang Normal University:Natural Sciences
基金 国家自然科学基金资助项目(10971194 11101374)
关键词 HARDY不等式 Sobolev—Hardy临界指数 变分方法 非平凡解 Hardy inequality Sobolev-Hardy critical exponents variational methods nontrivial solutions
分类号 O175.25 [理学—基础数学]
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参考文献12

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二级参考文献21

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浙江师范大学学报（自然科学版）
2013年 第1期

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