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Innovation in Qualitative Analysis of Nonlinear Differential Equations: Entering a New Phase of Nonlinear Oscillation Theory

Research Project

Project/Area Number 16K05238
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionOsaka Metropolitan University (2022-2023)
Osaka Prefecture University (2018-2021)
Kumamoto University (2016-2017)

Principal Investigator

TANIGAWA Tomoyuki  大阪公立大学, 大学院理学研究科, 教授 (10332008)

Project Period (FY) 2016-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords微分方程式の振動理論 / 非線形微分方程式の振動理論 / 正則変動関数論 / 非線形振動理論 / 正則変動関数の理論 / 微分方程式の振動性と非振動性 / 微分方程式の解の漸近挙動 / 微分方程式の解の漸近解析 / 微分方程式の非振動解の漸近挙動 / 非振動解の漸近解析 / Riccati 方程式 / 関数方程式 / 微分方程式論
Outline of Final Research Achievements

Nonlinear Sturm-Liouville differential operators (both non-neutral and neutral types) and their associated systems of differential equations: (a) Characterization of oscillatory behavior in nonlinear differential equations, (b) Effect of adding a non-purturbative term to a differential equations of non-oscillatory types, (c) Utilization of Regular Variation Theory for analyzing non-oscillatory solutions of various differential equations. Regular variation functions are a general term for a family of classes of functions classified according to certain criteria. (d) Relationship between non-oscillatory solutions of nonlinear differential equations and nonlinear Riccati equations, which provide useful informations such as the existence of non-oscillatory solutions. Explored the connection between non-oscillatory solutions of nonlinear differential equations and solutions of nonlinear Riccati equations.
Provided valuable insights into the existence of non-oscillatory solutions.

Academic Significance and Societal Importance of the Research Achievements

本研究課題の学術的意義: 非線形微分方程式の振動理論は, 自然現象や社会現象を記述する数理モデル(非線形微分方程式)の解の全体構造を解明することを目標に世界各国で長年研究されてきた分野である. その振動理論の進展に大きく寄与することができたと思える. また, 本来, 非線形微分方程式に対する解は具体的に表現することができないため, 上述のような振動理論を駆使して解の性質を捉えることが最善の手法になっている.
本研究の社会的意義: 歴史のある振動理論を活用することによって, 多種多様の微分方程式の解の特徴を入手することに成功することができ, 科学及び文明の進展に大きく貢献したと思われる.

Report

(9 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (39 results)

All 2023 2022 2021 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (12 results) Journal Article (14 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 10 results,  Open Access: 14 results,  Acknowledgement Compliant: 1 results) Presentation (12 results) (of which Int'l Joint Research: 3 results,  Invited: 9 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] University of Nis(セルビア)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of NIs(セルビア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Nis(セルビア)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of Nis(セルビア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of Nis(セルビア)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Comenius University(スロバキア)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Asymptotic analysis of solutions of second order quasilinear differential equations with variable exponents of nonlinearity.2023

    • Author(s)
      K. Fujimoto, M. Hamaoka and T. Tanigawa
    • Journal Title

      Memoirs on Differential Equations and Mathematical Physics

      Volume: 90 Pages: 1-13

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Extreme and moderate solutions of nonoscillatory second order half-linear differential equations2022

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      Annales Polonici Mathematici

      Volume: 128 Pages: 49-85

    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Oscillatory properties of solutions of second order half-linear differential equations2021

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      IWQUALITDE

      Volume: 2021 Pages: 83-86

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Structure of nonoscillatory solutions of second order half-linear differential equations2020

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      IWQUALITDE

      Volume: 2020 Pages: 99-101

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Oscillation criteria for fourth order half-linear differential equations2020

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      Archivum Mathematicum (Brno)

      Volume: 56 Issue: 2 Pages: 115-125

    • DOI

      10.5817/am2020-2-115

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Viewing nonoscillatory second order linear differential equations from the angle of Riccati equations2020

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      arXiv:2006.11592v1 Cornell University

      Volume: 2020 Pages: 1-27

    • Related Report
      2020 Research-status Report
    • Open Access / Int'l Joint Research
  • [Journal Article] Asymptotic analysis of two-dimensional cyclic systems of first order nonlinear differential equations2019

    • Author(s)
      Tomoyuki Tanigawa
    • Journal Title

      IWQUALITDE

      Volume: 2019

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Nonoscillatory solutions of planar half-linear differential systems: a Riccati equation approach.2018

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      Electronic Journal of Qualitative Theory of Differential Equations

      Volume: 92

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Productivity of Riccati differential equations2018

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      IWQUALITDE

      Volume: 2018 Pages: 67-71

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Existence of rapidly varying solutions of second order half-linear differential equations2017

    • Author(s)
      Tomoyuki Tanigawa
    • Journal Title

      IWQUALITDE

      Volume: 2017 Pages: 188-192

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Asymptotic analysis of positive solutions of a class of nonlinear differential equations in the framework of regular variation2017

    • Author(s)
      谷川智幸
    • Journal Title

      京都大学数理解析研究所「常微分方程式の定性的理論とその周辺」数理解析研究所講究録,

      Volume: 2032 Pages: 11-20

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] 数理モデルの援用による数学授業開発2017

    • Author(s)
      谷川智幸, 井上直哉, 澁谷明人
    • Journal Title

      熊本大学教育実践研究

      Volume: 34 Pages: 37-45

    • NAID

      120005983285

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] 高等学校数学から小学校算数へ向けての面積学習の応用2017

    • Author(s)
      谷川智幸, 佐藤英樹
    • Journal Title

      熊本大学教育学部紀要

      Volume: 66 Pages: 299-304

    • NAID

      120006380749

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] Regularly varying solutions with intermediate growth for cyclic differential systems of second order2017

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      Electoronic Journal of Differential Equations

      Volume: -

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Existence and Asymptotic Behavior of Nonoscillatory Solutions of Quasilinear Differential Equations with Variable Exponents2023

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      International Workshop on the Qualitative Theory of Differential Equations "QUALITDE 2023"
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Oscillatory properties of solutions of second order half-linear differential equations2021

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Organizer
      International Workshop QUALITDE
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Riccati 方程式を用いる半分線形微分方程式の非振動解の研究2020

    • Author(s)
      谷川智幸
    • Organizer
      日本数学会年会
    • Related Report
      2019 Research-status Report
  • [Presentation] Existence and precise asymptotic behavior of positive solutions of scalar and systems of nonlinear differential equations2018

    • Author(s)
      谷川智幸
    • Organizer
      第42回南大阪応用数学セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Existence and asymptotic behavior of positive solutions of second order half-linear functional differential equations in the framework of regular variations2017

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Conference on Differential and Difference Equations and Applications 2017, Jasna, Slovakia
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 正則変動関数論を活用した非線形微分方程式の漸近解析2017

    • Author(s)
      谷川智幸
    • Organizer
      なかもず解析セミナー(大阪府立大学)
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] ある非線形連立微分方程式の強減衰解と強増大解の存在について2017

    • Author(s)
      谷川智幸
    • Organizer
      愛媛大学における微分方程式セミナー(愛媛大学)
    • Related Report
      2017 Research-status Report
  • [Presentation] ある非線形関数微分方程式の一般化された緩変動解と指数1の正則変動解の存在について2017

    • Author(s)
      谷川智幸
    • Organizer
      富山解析セミナー(富山大学:第178回APセミナー)
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Asymptotic analysis of positive solutions of a class of nonlinear differential equations in the framework of regular variation2016

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Qualitative Theory of Ordinary Differential Equations and Related Area
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-11-16
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] ある非線形微分方程式の正値解の漸近挙動について2016

    • Author(s)
      谷川智幸
    • Organizer
      常微分方程式の定性的理論ワークショップ
    • Place of Presentation
      島根大学
    • Year and Date
      2016-09-22
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 正則変動関数論と微分方程式の解の漸近挙動2016

    • Author(s)
      谷川智幸
    • Organizer
      日本数学会秋季総合分科会(特別講演)
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Existence of regularly varying solutions of a class of third order nonlinear differential equations2016

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      富山解析セキナー(第177回APセミナー)
    • Place of Presentation
      富山大学
    • Related Report
      2016 Research-status Report
  • [Funded Workshop] RIMS Workshop Succession and Innovation of Studies on ODEs in Real Domains2017

    • Related Report
      2017 Research-status Report

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Published: 2016-04-21   Modified: 2025-01-30  

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