| The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group |
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| 引用本文： | ZHENG Zhu-jun,WANG Guo-an,LU Ke-ping,LUO Xue-bo(1. College of Mathematics and Information Science,Henan University,Kaifeng 475001,China, 2.Institute of Mathematics,Henan University,Kaifeng 475001,China, 3. Information Network Center,Henan University,Kaifeng 475001,China, 4. Institute of Applied Mathematics,Northwestern Ploytechnical University,Xi'an 710072,China). The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group[J]. 数学季刊, 2004, 19(4) |
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| 作者姓名： | ZHENG Zhu-jun WANG Guo-an LU Ke-ping LUO Xue-bo(1. College of Mathematics and Information Science Henan University Kaifeng 475001 China 2.Institute of Mathematics Henan University Kaifeng 475001 China 3. Information Network Center Henan University Kaifeng 475001 China 4. Institute of Applied Mathematics Northwestern Ploytechnical University Xi'an 710072 China) |
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| 作者单位： | 1. College of Mathematics and Information Science，Henan University，Kaifeng 475001，China; 2.Institute of Mathematics，Henan University，Kaifeng 475001，China; 3. Information Network Center，Henan University，Kaifeng 475001，China; 4. Institute of Applied Mathematics，Northwestern Ploytechnical University，Xi'an 710072，China |
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| 基金项目： | ThisworkiscompletedduringthefirstauthorvisitingtheInstituteofTheoreticalPhysics,ChineseAcademiaofSciencesthefirstauthorispartiallysupportedbytheNationalScienceFoundationofP.R.ChinaandoutstandingforYouthFoundationofHenanProvinceandtheNationalScienceFoundationofHenanProvince,P.R.China. |
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| 摘 要： | Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation-ΔHnu = |u|p-1u,x∈Hnhas infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.
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The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group |
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| ZHENG Zhu-jun,WANG Guo-an,LU Ke-ping,LUO Xue-bo. The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4) |
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| Authors: | ZHENG Zhu-jun WANG Guo-an LU Ke-ping LUO Xue-bo |
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| Abstract: | |
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| Keywords: | subelliptic operator Z2 index Heisenberg group generalized critical point |
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