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Stability analysis of standing waves for nonlinear Schrodinger equations

Research Project

Project/Area Number 23840037
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionTsuda College (2012)
Tokyo Denki University (2011)

Principal Investigator

KIKUCHI Hiroaki  津田塾大学, 学芸学部, 講師 (00612277)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords定在波 / 安定性 / 爆発 / 散乱 / 非線形楕円型方程式 / 特異解 / 分岐 / モース指数 / シュレディンガー方程式 / 定在波解 / 変分法 / 非線形シュレディンガー方程式 / 基底状態 / 励起状態 / 軌道安定性 / ポテンシャルの井戸
Research Abstract

In the academic year of 2011, I studied two kinds of subjects. One is concerned with a singular solution to nonlinear elliptic equations with the harmonic potential. Here, we consider the pure power nonlinearity with the Sobolev supercritical exponent. Th
In the academic year of 2012, we studied the scattering problem for the nonlinear Schrodinger equations with general nonlinearities. Here, we introduced a certain functional associated with the equations and assumed the nonlinearities satisfy the value of

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • Research Products

    (19 results)

All 2013 2012 2011 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (11 results) (of which Invited: 1 results) Remarks (1 results)

  • [Journal Article] Existence of a ground state and scattering for a nonlinear Schr\"{o}dinger equation with critical growth2013

    • Author(s)
      Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Hayato Nawa
    • Journal Title

      Selecta Math

      Volume: 19 Pages: 545-609

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of singular solution to stationary Schrodinger equation with supercritical nonlinearity2013

    • Author(s)
      Fouad Hadj Selem, Hiroaki Kikuchi, Juncheng Wei
    • Journal Title

      Discrete and Continuous Dynamical Systems-series A

      Volume: vol 33 Issue: 10 Pages: 4613-4626

    • DOI

      10.3934/dcds.2013.33.4613

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities2012

    • Author(s)
      Fouad Hadj Selem, Hiroaki Kikuchi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 387 Issue: 2 Pages: 746-754

    • DOI

      10.1016/j.jmaa.2011.09.034

    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of a ground state and blow-up problem for a nonlinear Schr\"{o}dinger equation with critical growth.2012

    • Author(s)
      Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Hayato Nawa
    • Journal Title

      Differential and Integral Equations

      Volume: 25 Pages: 383-402

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stationary problem related to the nonlinear Schrodinger equation on the unit ball2012

    • Author(s)
      Reika Fukuizumi, Fouad Hadj Selem and Hiroaki Kikuchi
    • Journal Title

      Nonlinearity

      Volume: vol 25 Issue: 8 Pages: 2271-2301

    • DOI

      10.1088/0951-7715/25/8/2271

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering and blowup problems for a class of nonlinear Schr\"{o}dinger equations2012

    • Author(s)
      Takafumi Akahori, Hiroaki Kikuchi, Hayato Nawa
    • Journal Title

      Differential and Integral Equations

      Volume: 25 Pages: 1075-1118

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of a ground state and blow-up problem for a nonlinear Schr¥"{o}dinger equation with critical growth2012

    • Author(s)
      Takafumi Akahori, Slim Ibrahim, Hiroaki kikuchi, Hayato Nawa
    • Journal Title

      Differential and Integral Equations

      Volume: 25 Pages: 383-402

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Blowup and scattering problems for a class of nonlinear Schrodinger equations2012

    • Author(s)
      Hiroaki Kikuchi
    • Organizer
      Analytical and Numerical Advances Around Schrodinger Equations
    • Place of Presentation
      Toulous (France)
    • Year and Date
      2012-10-26
    • Related Report
      2012 Final Research Report
  • [Presentation] ソボレフ超臨界の非線形項をもつ楕円型方程式の特異解の存在と一意性について2012

    • Author(s)
      菊池弘明
    • Organizer
      第103回神楽坂解析セミナー
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-05-26
    • Related Report
      2012 Final Research Report
  • [Presentation] Scattering and blowup problems for a class of nonlinear Schrodinger equations2012

    • Author(s)
      Hiroaki Kikuchi
    • Organizer
      Universite' Blaise Pascal (France)
    • Place of Presentation
      Universite' Blaise Pascal (France)
    • Year and Date
      2012-03-13
    • Related Report
      2012 Final Research Report
  • [Presentation] Scattering and blowup problems for a class of nonlinear Schrodinger equations2012

    • Author(s)
      菊池弘明
    • Organizer
      Seminar de Mathematiques Appliquees
    • Place of Presentation
      Blaise Pascal University
    • Year and Date
      2012-03-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] ソボレフ超臨界の非線形項をもつ楕円型方程式の特異解の存在と一意性について2012

    • Author(s)
      菊池弘明
    • Organizer
      第103回神楽坂解析セミナー
    • Place of Presentation
      東京理科大
    • Related Report
      2012 Annual Research Report
  • [Presentation] . Scattering and blowup problems for a class of nonlinear Schrodinger equations,2012

    • Author(s)
      菊池弘明
    • Organizer
      津田塾大学談話会
    • Place of Presentation
      津田塾大
    • Related Report
      2012 Annual Research Report
  • [Presentation] Blowup and scattering problems for a class of nonlinear Schrodinger equations,2012

    • Author(s)
      菊池弘明
    • Organizer
      Analytical and Numerical Advances Around Schrodinger Equations
    • Place of Presentation
      Universite Paul Sabatier
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Scattering and blowup problems for a class of nonlinear Schrodinger equations2011

    • Author(s)
      Hiroaki Kikuchi
    • Organizer
      the 4th MSJ-SI ``NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS"
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Scattering and blowup problems for a class of nonlinear Schrodinger equations2011

    • Author(s)
      菊池弘明
    • Organizer
      the 4th MSJ-SI "NONLINEAR DYNAMICS IN PAETIAL DIFFERENTIAL EQUATIONS"
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] 非線形シュレディンガー方程式の定在波の不安定性に関連する最小化問題について2011

    • Author(s)
      菊池弘明
    • Organizer
      OCAMI 楕円型方程式研究集会~定常非線形シュレディンガー方程式の定在波解の研究~
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-08-11
    • Related Report
      2012 Final Research Report
  • [Presentation] 非線形シュレディンガー方程式の定在波の不安定性に関連する最小化問題について2011

    • Author(s)
      菊池弘明
    • Organizer
      OCAMI楕円型方程式研究集会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2011-08-11
    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.sie.dendai.ac.jp/~hiroaki/

    • Related Report
      2011 Annual Research Report

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Published: 2011-09-05   Modified: 2019-07-29  

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