Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation

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...

Full description

Bibliographic Details
Main Authors: Yisheng Huang, Zeng Liu, Yuanze Wu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/398164
id doaj-728a43dc7c814c9ea7d885451710382c
record_format Article
spelling doaj-728a43dc7c814c9ea7d885451710382c2020-11-24T22:16:33ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Yisheng Huang
Zeng Liu
Yuanze Wu
spellingShingle Yisheng Huang
Zeng Liu
Yuanze Wu
Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation
Abstract and Applied Analysis
author_facet Yisheng Huang
Zeng Liu
Yuanze Wu
author_sort Yisheng Huang
title 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_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_sort existence of prescribed l2-norm solutions for a class of schrödinger-poisson equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
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].
url http://dx.doi.org/10.1155/2013/398164
work_keys_str_mv AT yishenghuang existenceofprescribedl2normsolutionsforaclassofschrodingerpoissonequation
AT zengliu existenceofprescribedl2normsolutionsforaclassofschrodingerpoissonequation
AT yuanzewu existenceofprescribedl2normsolutionsforaclassofschrodingerpoissonequation
_version_ 1725789215844728832

Similar Items