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Study of stability properties for positive linear equations with delay and related topics

Research Project

Project/Area Number 19540203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOkayama University of Science

Principal Investigator

MURAKAMI Satoru  Okayama University of Science, 理学部, 教授 (40123963)

Co-Investigator(Kenkyū-buntansha) KAMIYA Shigeyasu  岡山理科大学, 工学部, 教授 (80122381)
HAMAYA Yoshihiro  岡山理科大学, 総合情報学部, 教授 (40228549)
NAGABUCHI Yutaka  岡山理科大学, 理学部, 教授 (60252607)
TANAKA Satoshi  岡山理科大学, 理学部, 准教授 (90331959)
SHIMENO Nobukazu  岡山理科大学, 理学部, 准教授 (60254140)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords関数方程式 / 関数微分方程式 / 正の方程式 / 安定性 / 漸近挙動 / ボルテラ差分方程式 / 特性方程式 / スポクトル / スペクトル / 積分微分方程式
Research Abstract

We studied qualitative properties of solutions in functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay. Applying the variation-of-constants formula in the phase space for functional differential equations, we obtained a result on the behavior of solutions for equations with a perturbation. Also, we established a result on the existence of several invariant manifolds for nonlinear functional differential equations. Furthermore, treating integrodifferential equations mainly, we investigated the positivity of equations, and obtained a criterion on stabilities for positive equations.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (20 results)

All 2009 2008 2007

All Journal Article (19 results) (of which Peer Reviewed: 18 results) Presentation (1 results)

  • [Journal Article] On positive linear Volterra-Stieltjes differential systems2009

    • Author(s)
      P.H.A. Pham, S. Murakami, T. Naito, J.S. Shin, Y. Nagabuchi
    • Journal Title

      Integral Equations and Operator Theory Vol.64

      Pages: 325-355

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and robust stability of positive linear Volterra difference equations2009

    • Author(s)
      P.H.A. Pham, T. Naito, J.S. Shin, S. Murakami
    • Journal Title

      Intern. J. Robust and Nonlinear Control Vol.19

      Pages: 552-568

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stabilities with respect to a weight function in Volterra difference equations2009

    • Author(s)
      S. Murakami
    • Journal Title

      Advanced Studies in Pure Math. Vol.53

      Pages: 189-197

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On positive linear Volterra-Stieltjes differential systems2009

    • Author(s)
      Pham Huu Anh Ngoc
    • Journal Title

      Integral Equations and Operator Theory 64

      Pages: 325-355

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stabilities with respect to a weight function in Volterra difference equations2009

    • Author(s)
      Satoru Murakami
    • Journal Title

      Advanced Studies in Pure Mathematics 53

      Pages: 189-197

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability and robust stability of positive linear Volterra difference equations2009

    • Author(s)
      Pham Hun Anh Ngoc
    • Journal Title

      Intern.J.Robust and Nonlinear Control 19

      Pages: 552-568

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On stability and robust stability of positive linear Volterra equations2008

    • Author(s)
      P.H.A. Pham, T. Naito, J.S. Shin, S. Murakami
    • Journal Title

      SIAM J. Control Optimization Vol.47

      Pages: 975-996

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Positivity and stability of linear Volterra integro-differential equations in a Banach lattice2008

    • Author(s)
      S. Murakami, P.H.A. Pham
    • Journal Title

      RIMS Kokyuroku Vol.41582

      Pages: 23-32

    • Related Report
      2009 Final Research Report
  • [Journal Article] Perron type theorems for functional differetial equations with infinite delay in a Banach space2008

    • Author(s)
      K. Matsui, H. Matsunaga, S. Murakami
    • Journal Title

      Nonlinear Anal. Vol.69

      Pages: 3821-3837

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniform asymptotic stability and robust stability for positive linear Volterra difference equations in Banach lattices2008

    • Author(s)
      S. Murakami, Y. Nagabuchi
    • Journal Title

      Advances in Difference Equations Vol.2008

      Pages: 1-15

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On stability and robust stability of positive linear Volterra equations2008

    • Author(s)
      Pham Huu Anh Ngoc
    • Journal Title

      SIAM J. Control Optimization 47

      Pages: 975-996

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perron type theorems for functional differential equations with infinite delay in a Banach space2008

    • Author(s)
      Kazuyuki Matsui
    • Journal Title

      Nonlinear Analysis 69

      Pages: 3821-3837

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniform asymptotic stability and robust stability for positive linear Volterra difference equations2008

    • Author(s)
      Satoru Murakami
    • Journal Title

      Advances in Difference Equations 2008

      Pages: 1-15

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of positive linear integro-differential systems2007

    • Author(s)
      T. Naito, S. Murakami, J.S. Shin, P.H.A. Pham
    • Journal Title

      Integral Equations and Operator Theory Vol.58

      Pages: 255-272

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of linear integral equations with nonnegative kernels2007

    • Author(s)
      T. Naito, J.S. Shin, S. Murakami, P.H.A. Ngoc
    • Journal Title

      J. Math. Anal. Appl. Vol.335

      Pages: 298-313

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Invariant manifolds for abstract functional differential equations and related Volterra difference equations2007

    • Author(s)
      S. Murakami, Y. Nagabuchi
    • Journal Title

      Funkcial. Ekvac. Vol.50

      Pages: 133-170

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Invariant manifolds for abstract functional differential equations and related Volterra difference equations in a Banach space2007

    • Author(s)
      Satoru Murakami
    • Journal Title

      Funkcial.Ekvac. 50

      Pages: 133-170

    • NAID

      130000140684

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of linear integral equations with nonnegative kernels2007

    • Author(s)
      Toshiki Naito
    • Journal Title

      J.Math.Anal.Appl. 335

      Pages: 298-313

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of positive linear Volterra intgro-differential systems2007

    • Author(s)
      Toshiki Naito
    • Journal Title

      Integral Equations and Operator Theory 58

      Pages: 255-272

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Positivity and stability of linear Volterra integro-differential equations in a Banach lattice2007

    • Author(s)
      S. Murakami
    • Organizer
      研究集会「関数方程式論におけるモデリングと複素解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-11-05
    • Related Report
      2009 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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