Heisenberg群上无穷远处的集中列紧原理和具有Sobolev临界指数的p - 次Laplace方程多解的存在性 |
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引用本文: | 窦井波,郭千桥. Heisenberg群上无穷远处的集中列紧原理和具有Sobolev临界指数的p - 次Laplace方程多解的存在性[J]. 数学物理学报(A辑), 2009, 29(4): 1033-1043 |
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作者姓名: | 窦井波 郭千桥 |
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作者单位: | 窦井波(西安财经学院统计学院,西安,710061);郭千桥(西北工业大学应用数学系,西安,710072) |
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基金项目: | 陕西省自然科学基础研究计划,西北工业大学科技创新基金 |
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摘 要: | 通过建立Heisenberg群上无穷远处的集中列紧原理, 研究了如下$p$ -次Laplace方程-ΔH, pu=λg(ξ)|u|q-2u+f (ξ)|u|p*-2u,在Hn上,u∈ D1, p(Hn),其中ξ∈Hn,λ∈R,1 j, 且m, j为整数.
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关 键 词: | Heisenberg 群 p -次Laplace算子 集中列紧原理 Palais-Smale条件 多解 |
收稿时间: | 2008-04-18 |
修稿时间: | 2009-05-27 |
A Concentration-Compactness Principle at Infinity on the Heisenberg Group and Multiplicity of Solutions for p-sub-Laplacian Problem Involving Critical Sobolev Exponents |
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Affiliation: | (1.School of Statistics, Xi'an Institute of Finance and Economics, Xi'an 710061, 2.Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072) |
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Abstract: | The main results of this paper establish the concentration-compactness principle at infinity on the Heisenberg group. The authors considerthe p-sub-Laplacian problem involving critical Sobolev exponents -ΔH, pu=λg(ξ)|u|q-2u+f (ξ)|u|p*-2u, in Hn, u ∈ D1, p(Hn), where ξ ∈ Hn, λ ∈ R,1 j, both m and j are integers. The concentration-compactness principle allows to prove the Palais-Smale condition is satisfied below a certain level. |
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Keywords: | Heisenberg groupzz p-sub-Laplacianzz Concentration-compactness principlezz Palais-Smale conditionzz Multiplicityzz |
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