Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation
By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)∫ℝ3|∇u|2dx+(1/4)∬ℝ3(|u(x)|2|u(y)|2/|x-y|)dx dy − (1/p)∫ℝ3|u|pdx:u∈Bρ} can be achieved for p∈(2,3) and ρ>0 small, where Bρ:={u∈H1(ℝ3):∥u∥2=ρ}. Moreover, the properties of Iρ2/ρ2 a...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/398164 |
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| author | Yisheng Huang Zeng Liu Yuanze Wu |
| author_facet | Yisheng Huang Zeng Liu Yuanze Wu |
| author_sort | Yisheng Huang |
| collection | DOAJ |
| description | By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)∫ℝ3|∇u|2dx+(1/4)∬ℝ3(|u(x)|2|u(y)|2/|x-y|)dx dy − (1/p)∫ℝ3|u|pdx:u∈Bρ} can be achieved for p∈(2,3) and ρ>0 small, where Bρ:={u∈H1(ℝ3):∥u∥2=ρ}. Moreover, the properties of Iρ2/ρ2 and the associated Lagrange multiplier λρ are also given if p∈(2,8/3]. |
| format | Article |
| id | doaj-art-728a43dc7c814c9ea7d885451710382c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-728a43dc7c814c9ea7d885451710382c2025-02-03T06:01:11ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/398164398164Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson EquationYisheng Huang0Zeng Liu1Yuanze Wu2Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, ChinaDepartment of Mathematics, Soochow University, Suzhou, Jiangsu 215006, ChinaCumt College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, ChinaBy using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)∫ℝ3|∇u|2dx+(1/4)∬ℝ3(|u(x)|2|u(y)|2/|x-y|)dx dy − (1/p)∫ℝ3|u|pdx:u∈Bρ} can be achieved for p∈(2,3) and ρ>0 small, where Bρ:={u∈H1(ℝ3):∥u∥2=ρ}. Moreover, the properties of Iρ2/ρ2 and the associated Lagrange multiplier λρ are also given if p∈(2,8/3].http://dx.doi.org/10.1155/2013/398164 |
| spellingShingle | Yisheng Huang Zeng Liu Yuanze Wu Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation Abstract and Applied Analysis |
| title | Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation |
| title_full | Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation |
| title_fullStr | Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation |
| title_full_unstemmed | Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation |
| title_short | Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation |
| title_sort | existence of prescribed l2 norm solutions for a class of schrodinger poisson equation |
| url | http://dx.doi.org/10.1155/2013/398164 |
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