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Study of the solution semigroup for integral equations and related topics

Research Project

Project/Area Number 22540211
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  岡山理科大学, 理学部, 教授 (40123963)

Co-Investigator(Kenkyū-buntansha) 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)
KAMIYA Shigeyasu  岡山理科大学, 工学部, 教授 (80122381)
TANAKA Satoshi  岡山理科大学, 理学部, 准教授 (90331959)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords積分方程式 / 解半群 / スペクトル / 定数変化法の公式 / 安定性 / 中心多様体 / 中心方程式 / 相空間 / 線形化原理 / 特性方程式 / 漸近挙動 / ボルテラ方程式
Research Abstract

We studied some qualitative properties of solutions in integral equations. Indeed, for linear integral equations we analyzed some spectral properties for the generator of the associated solution semigroup, and obtained an estimate on the essential spectral radius of the generator. Furthermore, we established a representation formula in the phase space for solutions of nonhomogeneous linear equations. Applying these results, we obtained Massera type results on the existence of bounded solutions, periodic solutions and so on. Also, for nonlinear integral equations we established the principle of linearization which is effectively applicable to stability problems in nonlinear equations.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (17 results)

All 2012 2011 2010

All Journal Article (11 results) (of which Peer Reviewed: 9 results) Presentation (6 results) (of which Invited: 1 results)

  • [Journal Article] Decomposition and variation-of-constants formula in the phase space for integral equations2012

    • Author(s)
      H. Matsunaga, S. Murakami and N.V.Minh
    • Journal Title

      Funkcial. Ekvacioj

      Volume: Vol.55 Pages: 479-520

    • NAID

      130002516279

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Formal adjoint equations and asymptotic formula for solutions of Volterra difference equations with infinite delay2012

    • Author(s)
      H. Matsunaga, S. Murakami, Y. Nagabuchi and Y. Nakano
    • Journal Title

      J. Difference Equations and Applications

      Volume: Vol.18 Pages: 57-88

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and instability lineariza- tion for integral equations2012

    • Author(s)
      H. Matsunaga, S. Murakami and N.V. Minh
    • Journal Title

      RIMS Kokyuroku

      Volume: Vol.1786 Pages: 66-84

    • Related Report
      2012 Final Research Report
  • [Journal Article] Decomposition and variation-of-constants formula in the phase space forintegral equations2012

    • Author(s)
      Hideaki Matsunaga
    • Journal Title

      Funkcial. Ekvacioj

      Volume: 55 Pages: 479-520

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability and instability linearization for integral equations2012

    • Author(s)
      Hideaki Matsunaga
    • Journal Title

      RIMS Kokyuroku

      Volume: 1786 Pages: 66-84

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Formal adjoint equations and asymptotic formula for solutions of Volterra difference equations with infinite delay2012

    • Author(s)
      Hideaki Matsunaga
    • Journal Title

      Journal of Difference Equations and Applications

      Volume: 18 Pages: 57-88

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability properties and almost periodic solutions of abstract functional differential equations with infinite delay2011

    • Author(s)
      Y. Hamaya
    • Journal Title

      Libertys Mathematica

      Volume: Vol.16 Pages: 93-102

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On stability and robust stability of positive linear Volterra equations in Banach spaces2010

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

      Central European Journal of Math.

      Volume: Vol.8 Pages: 966-984

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fower differ-ential equations2010

    • Author(s)
      S. Tanaka
    • Journal Title

      Mathematica Bohemica

      Volume: Vol.135 Pages: 189-198

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Notes on complex hyperbolic triangle groups2010

    • Author(s)
      S. Kamiya
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: Vol.14 Pages: 202-218

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On stability and robust stability of positive linear Volterra equations in Banach lattices2010

    • Author(s)
      Satoru Murakami
    • Journal Title

      Central European Journal of Mathematics

      Volume: 8 Pages: 966-984

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Linearized stability and instability principle for integral equations2012

    • Author(s)
      S. Murakami
    • Organizer
      研究集会「関数微分方程式の定性的理論の新展 開」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-11-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Center manifold theorem for integral equations2012

    • Author(s)
      S. Murakami
    • Organizer
      研究集会「常微分方程式の大域的理論とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-11-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Center manifold theorem for integral equations2012

    • Author(s)
      村上 悟
    • Organizer
      常微分方程式の大域的定性理論とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Linearized stability and instability principle for integral equations2011

    • Author(s)
      村上悟
    • Organizer
      関数微分方程式の定性的理論の新展開
    • Place of Presentation
      京都大学数理解析研究所[京都府](招待講演)
    • Year and Date
      2011-11-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] 線形積分方程式に対する解半群のスペク トルの性質、双線形形式および解の漸近公式2011

    • Author(s)
      S. Murakami
    • Organizer
      研究集会「微分方程式の定性的理論ワークショップ in 岡山理大」
    • Place of Presentation
      岡山理科大学25号館
    • Year and Date
      2011-01-23
    • Related Report
      2012 Final Research Report
  • [Presentation] 線形積分方程式に対する解半群のスペクトルの性質,双線形形式および解の漸近公式2011

    • Author(s)
      村上悟
    • Organizer
      微分方程式の定性的理論ワークショップin岡山理大
    • Place of Presentation
      岡山理科大学25号館(岡山県)(招待講演)
    • Year and Date
      2011-01-23
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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