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Precise asymptotic analysis of solutions of nonlinear differential equations by means of regular variation: The theoretical face and back sides for oscillation theory

Research Project

Project/Area Number 23540218
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKumamoto University

Principal Investigator

Tanigawa Tomoyuki  熊本大学, 教育学部, 准教授 (10332008)

Project Period (FY) 2011-04-28 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords微分方程式論 / 振動理論 / 非振動解の漸近挙動 / 正則変動関数論 / 微分方程式 / 国際研究者交流 / 多国籍
Outline of Final Research Achievements

The purpose of this research subject is devoted to the asymptotic analysis of the nonoscillatory behavior of several types of the nonlinear differential equations. Our main results obtained are as belows.
(1) The existence and the asymptotic behavior for the large value of the variable of the positive solutions of generalized Thomas-Fermi equation are proved. (2) We establish a sharp condition of the existence of generalized regularly varying functions (in the sense of Karamata) of self-adjoint functional differential equation. (3) We devote to the asymptotic analysis of a class of the third order sublinear differential equation. (4) We demonstrate that the method of regular variation can be effectively applied to fourth order quasilinear differential equations. (5) We show that an application of the theory of regular variation gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third order nonlinear differential equation

Report

(6 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (35 results)

All 2016 2015 2014 2013 2012 2011 Other

All Journal Article (13 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 13 results,  Open Access: 6 results,  Acknowledgement Compliant: 6 results) Presentation (22 results) (of which Int'l Joint Research: 3 results,  Invited: 9 results)

  • [Journal Article] Asymptotic analysis of positive decreasing solutions of a class of systems of second order nonlinear differential equations in the framework of regular variation2015

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

      The Australian Journal of Mathematical Analysis and Applications

      Volume: 12

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Existence and asymptotic behavior of strongly monotone solutions of nonlinear differential equations2015

    • Author(s)
      Tomoyuki Tanigawa
    • Journal Title

      Differential Equations and Applications

      Volume: 7 Issue: 1 Pages: 79-91

    • DOI

      10.7153/dea-07-06

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Regularly varying solutions of half-linear differential equations with retarded and advanced arguments2015

    • Author(s)
      J. Manojlovic and T. Tanigawa
    • Journal Title

      Mathematica Slovaca

      Volume: 65

    • Related Report
      2015 Annual Research Report 2014 Research-status Report 2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Asymptotic analysis of positive decreasing solutions of a class of systems of second order nonlinear differential equations in the framework of regular variation.2015

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

      The Australian Journal of Mathematical Analysis and Applications

      Volume: 12

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Existence and asymptotic behavior of strongly monotone solutions of nonlinear differential equations.2015

    • Author(s)
      Tomoyuki Tanigawa
    • Journal Title

      Differential Equations and Applications

      Volume: 7 Pages: 79-91

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Asymptotic analysis of positive solutions of third order nonlinear differential equations2014

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

      Hiroshima Mathematical Journal

      Volume: 44

    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Existence and asymptotic behavior of positive solutions of fourth order quasilinear differential equations2013

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

      Taiwanese Journal of Mathematics

      Volume: 17 Pages: 999-1030

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence and precise asymptotics of positive solutions for a class of nonlinear differential equations of the third order2013

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

      Georgian Mathematical Journal

      Volume: 20 Pages: 493-531

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis of positive solutions of third order nonlinear differential equations2013

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

      Hiroshima Mathematical Journal

      Volume: 印刷中

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized regularly varying solutions of second order nonlinear differential equations with deviating arguments2012

    • Author(s)
      Tomoyuki Tanigawa
    • Journal Title

      Memoirs on Differential Equations and Mathematical Physics

      Volume: 57

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis of positive solutions of a class of third order nonlinear differential equations in the framework of regular variation2012

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

      Mathematische Nachrichten

      Volume: 286 Issue: 2-3 Pages: 205-223

    • DOI

      10.1002/mana.201100296

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] An asymptotic analysis of positive solutions of generalized Thomas--Fermi differential equations -- The sub-half-linear case2012

    • Author(s)
      Takasi Kusano, Vojislav Maric and Tomoyuki Tanigawa
    • Journal Title

      Nonlinear Analysis: Theory, Methods & Applications

      Volume: 75

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sharp oscillation criteria for a class of fourth order nonlinear differential equations2011

    • Author(s)
      Takasi Kusano, Jelena Manojlovic and Tomoyuki Tanigawa
    • Journal Title

      The Rocky Mountain Journal of Mathematics

      Volume: 41

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 混合型2階半分線形関数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
      日本数学会年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] Asymptotic behavior of positive solutions of second order half-linear differential equations with deviating arguments of mixed type2015

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      International Workshop on the Qualitative Theory of Differential Equations, QUALITDE 2015
    • Place of Presentation
      Tbilisi, Georgia
    • Year and Date
      2015-12-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Existence and asymptotic behavior of strongly monotone solutions of nonlinear differential equations2015

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      The Equadiff 2015
    • Place of Presentation
      Lyon, France
    • Year and Date
      2015-07-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Asymptotic analysis of strongly monotone solutions of nonlinear differential equations2015

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Conference on Differential \& Difference Equations and Applications
    • Place of Presentation
      Lisbon, Portugal
    • Year and Date
      2015-05-18
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 4階劣半分線形微分方程式の正値解の存在について2015

    • Author(s)
      谷川智幸
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] ある4 階非線形微分方程式の正則変動関数解の存在について2015

    • Author(s)
      谷川智幸
    • Organizer
      常微分方程式ワークショップ
    • Place of Presentation
      愛媛大学
    • Year and Date
      2015-03-10
    • Related Report
      2014 Research-status Report
  • [Presentation] 正則変動関数論の微分方程式への応用2015

    • Author(s)
      谷川智幸
    • Organizer
      第7回半田山微分方程式セミナー
    • Place of Presentation
      岡山理科大学
    • Year and Date
      2015-02-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 3 階 Emden - Fowler 型微分方程式の正値解の漸近挙動について2014

    • Author(s)
      谷川智幸
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 遅れの変数を含む2階半分線形微分方程式の零でない指数の正則変動関数解の存在について2014

    • Author(s)
      谷川智幸
    • Organizer
      振動理論ワークショップ -- 金沢 2013
    • Place of Presentation
      金沢大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Asymptotic analysis of positive decreasing solutions of a class of systems of second order nonlinear differential equations in the framework of regular variation2013

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      The Equadiff 13 conference 2013
    • Place of Presentation
      Prague, Czech Republic
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Asymptotic behavior of decreasing solutions of a class of systems of second order nonlinear differential equations2013

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Colloquium on Differential Equations
    • Place of Presentation
      Nis, Serbia
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 2階非線形微分方程式系の正値減少解について2013

    • Author(s)
      谷川智幸
    • Organizer
      岡山理科大学における微分方程式セミナー
    • Place of Presentation
      岡山理科大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 進みと遅れの変数を含む2階半分線形関数微分方程式の一般化された正則変動関数解の存在について2013

    • Author(s)
      谷川智幸
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ある2階非線形微分方程式系の正値減少解の漸近挙動について2013

    • Author(s)
      谷川智幸
    • Organizer
      第174回 AP Seminar (研究集会「富山解析セミナー2013」)
    • Place of Presentation
      富山大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ある3階非線形微分方程式の正値解の漸近挙動について2013

    • Author(s)
      谷川智幸
    • Organizer
      振動理論ワークショップ ー 松山  2013
    • Place of Presentation
      愛媛大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Generalized regularly varying solutions of half-linear functional differential equations with retarded and advanced arguments2012

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Conference on Differential and Difference Equations and Applications
    • Place of Presentation
      スロバキア(ジリナ)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 進みと遅れの変数をもつ2 階半分線形関数微分方程式の正値解について2012

    • Author(s)
      谷川智幸
    • Organizer
      愛知教育大学における微分方程式セミナー
    • Place of Presentation
      愛知教育大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 微分方程式の解の漸近挙動とKaramata 関数について2012

    • Author(s)
      谷川智幸
    • Organizer
      第21 回岐阜数理科学セミナー
    • Place of Presentation
      岐阜大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Precise asymptotic behavior of positive solutions of generalized Thomas -- Fermi differential equations2011

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Progress in Qualitative Theory of Functional Equations(招待講演)
    • Place of Presentation
      Research Institute for Mathematical Sciences Conference, Kyoto University
    • Related Report
      2011 Research-status Report
  • [Presentation] 一般化された Thomas - Fermi 型微分方程式の正則変動解の漸近解析について

    • Author(s)
      谷川智幸
    • Organizer
      岐阜大学における微分方程式セミナー(招待講演)
    • Place of Presentation
      岐阜大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 一般化された Thomas - Fermi 型微分方程式の解の漸近解析について

    • Author(s)
      谷川智幸
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] ある非半分線形微分方程式の解の漸近挙動について

    • Author(s)
      谷川智幸
    • Organizer
      富山解析セミナー 2011(招待講演)
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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