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Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation
Joint Authors
Liu, Zeng
Huang, Yisheng
Wu, Yuanze
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-12
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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].
American Psychological Association (APA)
Huang, Yisheng& Liu, Zeng& Wu, Yuanze. 2013. Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-468990
Modern Language Association (MLA)
Huang, Yisheng…[et al.]. Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation. Abstract and Applied Analysis No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-468990
American Medical Association (AMA)
Huang, Yisheng& Liu, Zeng& Wu, Yuanze. Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-468990
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468990