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

• Project/Area Number: 20740091
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Shizuoka 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: ¥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.

Research Products

• [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation (2011)
  • Author(s): 足達慎二, 渡辺達也
  • Journal Title: Advances in Differential Equations Vol.16 Pages: 289-324
  • Peer Reviewed
• [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation (2011)
  • Author(s): Shinji Adachi, Tatsuya Watanabe
  • Journal Title: Advances in Differential Equations Volume: 16 Pages: 289-324
  • Peer Reviewed
• [Journal Article] Uniqueness of the ground state solutions of quasilinear Schrodinger equations (2010)
  • Author(s): Shinji Adachi, Tatsuya Watanabe
  • Journal Title: Osaka City University Mathematical Preprint Series 9-19
• [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation (2009)
  • Author(s): Shinji Adachi, Tatsuya Watanabe
  • Journal Title: Osaka City University Mathematical Preprint Series 9-17
• [Presentation] Uniqueness of positive radial solutions of quasilinear Schrodinger equation (2010)
  • 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
• [Presentation] G-invariant positive solutions for a quasilinear Schrodinger equation (2010)
  • 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
• [Presentation] Existence and uniqueness of ground states for a quasilinear Schrodinger equation (2010)
  • 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
• [Presentation] Existence and uniqueness of ground states for a quasilinear Schrodinger equation (2010)
  • 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
• [Presentation] Existence of G-invariant standing waves of quasilinear Schrodinger equations (2010)
  • 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
• [Presentation] Existence of G-invariant standing waves of quasilinear Schro dinger equations (2010)
  • 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
• [Presentation] On the existence of G-invariant standing waves for a class of quasilinear Schrodinger equations (2009)
  • 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
• [Presentation] Existence of positive solutions for a class of quasilinear elliptic equations (2009)
  • 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
• [Remarks] ホームページ等
  • URL: http://www.ipc.shizuoka.ac.jp/~tsadati/