| BOUND STATES FOR A STATIONARY NONLINEAR SCHRODINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3△ |
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| 引用本文： | 蒋永生,周焕松.BOUND STATES FOR A STATIONARY NONLINEAR SCHRODINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3△[J].数学物理学报(B辑英文版),2009,29(4):1095-1104. |
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| 作者姓名： | 蒋永生 周焕松 |
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| 基金项目： | This work was supported by NSFC （10631030） and CAS-KJCX3-SYW-S03. |
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| 摘 要： | We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0
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| 关 键 词： | 非线性 系统 松 注册商标 巴勒斯坦 薛定谔 合订本 名称 |
BOUND STATES FOR A STATIONARY NONLINEAR SCHRODINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3△ |
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| Jiang Yongsheng,Zhou Huansong.BOUND STATES FOR A STATIONARY NONLINEAR SCHRODINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3△[J].Acta Mathematica Scientia,2009,29(4):1095-1104. |
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| Authors: | Jiang Yongsheng Zhou Huansong |
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| Institution: | Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences P.O.Box 71010, Wuhan 430071, China |
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| Abstract: | Schrodinger-Poisson system sub-supersolutions supercritical Sobolev expo-nent sign-changing potential bound state |
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| Keywords: | Schrodinger-Poisson system sub-supersolutions supercritical Sobolev expo-nent sign-changing potential bound state |
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