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A variational study on the multiple existence of periodic orbits for some singular Hamiltonian system

Research Project

Project/Area Number 20740091
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionShizuoka University

Principal Investigator

ADACHI Shinji  Shizuoka University, 工学部, 准教授 (40339685)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords変分法 / 特異ハミルトン系 / 非衝突周期軌道 / 楕円型方程式 / 正値解 / 準線形楕円型方程式 / 一意性 / 変分的手法 / G-不変 / Morse Index / 周期軌道 / 非衝突性 / 準線形性 / dual approach
Research Abstract

I obtain precise estimate of the Morse index for some class of singular Hamiltonian system, which is a key point for the multiple existence of periodic orbits. I also show the existence of G-invariant positive solution of some quasilinear elliptic equations arising from plasma physics.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (13 results)

All 2011 2010 2009 Other

All Journal Article (4 results) (of which Peer Reviewed: 2 results) Presentation (8 results) Remarks (1 results)

  • [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation2011

    • Author(s)
      足達慎二, 渡辺達也
    • Journal Title

      Advances in Differential Equations Vol.16

      Pages: 289-324

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation2011

    • Author(s)
      Shinji Adachi, Tatsuya Watanabe
    • Journal Title

      Advances in Differential Equations

      Volume: 16 Pages: 289-324

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness of the ground state solutions of quasilinear Schrodinger equations2010

    • Author(s)
      Shinji Adachi, Tatsuya Watanabe
    • Journal Title

      Osaka City University Mathematical Preprint Series 9-19

    • Related Report
      2009 Annual Research Report
  • [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation2009

    • Author(s)
      Shinji Adachi, Tatsuya Watanabe
    • Journal Title

      Osaka City University Mathematical Preprint Series 9-17

    • Related Report
      2009 Annual Research Report
  • [Presentation] Uniqueness of positive radial solutions of quasilinear Schrodinger equation2010

    • Author(s)
      渡辺達也, 足達慎二
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] G-invariant positive solutions for a quasilinear Schrodinger equation2010

    • Author(s)
      渡辺達也, 足達慎二
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Existence and uniqueness of ground states for a quasilinear Schrodinger equation2010

    • Author(s)
      足達慎二
    • Organizer
      第4回非線形偏微分方程式と変分問題
    • Place of Presentation
      首都大学東京
    • Year and Date
      2010-02-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Existence and uniqueness of ground states for a quasilinear Schrodinger equation2010

    • Author(s)
      足達慎二
    • Organizer
      第4回非線型偏微分方程式と変分問題
    • Place of Presentation
      首都大学東京
    • Year and Date
      2010-02-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] Existence of G-invariant standing waves of quasilinear Schrodinger equations2010

    • Author(s)
      足達慎二
    • Organizer
      変分セミナー
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-01-09
    • Related Report
      2010 Final Research Report
  • [Presentation] Existence of G-invariant standing waves of quasilinear Schro dinger equations2010

    • Author(s)
      足達慎二
    • Organizer
      変分セミナー
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-01-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the existence of G-invariant standing waves for a class of quasilinear Schrodinger equations2009

    • Author(s)
      足達慎二
    • Organizer
      第35回発展方程式研究会
    • Place of Presentation
      中央大学
    • Year and Date
      2009-12-23
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Existence of positive solutions for a class of quasilinear elliptic equations2009

    • Author(s)
      足達慎二
    • Organizer
      第3回非線型偏微分方程式と変分問題
    • Place of Presentation
      首都大学東京
    • Year and Date
      2009-02-15
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.ipc.shizuoka.ac.jp/~tsadati/

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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