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Formal adjoint equation for equations with time delay and its applications

Research Project

Project/Area Number 16540177
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, Department of Applied Mathematics, Professor, 理学部, 教授 (40123963)

Co-Investigator(Kenkyū-buntansha) KAMIYA Shigeyasu  Okayama University of Science, Department of Intelligent Mechanical Engineering, Professor, 工学部, 教授 (80122381)
HAMAYA Yoshihiro  Okayama University of Science, Department of Information Science, Professor, 総合情報学部, 教授 (40228549)
SHIMENO Nobukazu  Okayama University of Science, Department of Applied Mathematics, Associate Professor, 理学部, 准教授 (60254140)
NAGABUCHI Yutaka  Okayama University of Science, Department of Applied Science, Associate Professor, 理学部, 准教授 (60252607)
TANAKA Satoshi  Okayama University of Science, Department of Applied Mathematics, Lecturer, 理学部, 講師 (90331959)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
KeywordsFunctional Differential Equations / Functional Difference Equations / Phase space / Stabilities / Almost periodic solutions / Solution operators / Variation-of-constans formula / Asymptotic behavior / スペクトル / 積分微分方程式 / ボルテラ差分方程式
Research Abstract

Head investigator and five investigators studied qualitative properties of solutions of functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay, and obtained many results on the subject as cited below.
1. For linear integrodifferential equations with integrable kernels, we characterized uniform asymptotic stability property of the zero solution in terms of the distribution of spectrum of the characteristic operator as wellas the integrability of the resolvent. As an application of the result, for equations with almost periodic perturbation we obtained a sufficient condition for the existence of almost periodic solutions, and analyzed the spectrum of the almost periodic solutions. Furthermore, applying the method to Volterra difference equations, we obtained some result on the stability property of the solution of partial differential equations with piecewise continuous delay.
2. Using a variation-of-constants formula in the phase space for linear equations with delay, we established the existence of invariant manifolds (such as local stable manifold, local center manifold and so on) for some nonlinear equations, and applied the result to the stability problem. Also, through some finer considerations, we investigated the smoothness of the invariant manifolds.
3. For linear functional difference equations with perturbations, we investigated the asymptotic behavior of solutions by decomposing the phase space into the direct sum of the stable subspace and the unstable manifold by means of the spectrum analysis of the solution operator, and obtained an extension of the Perron theorem for ordinary differential equations.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (38 results)

All 2007 2006 2005 2004 Other

All Journal Article (38 results)

  • [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. 50

      Pages: 133-170

    • NAID

      130000140684

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Characterization of linear integral equations with nonnegati kernels2007

    • Author(s)
      Toshiki Naito
    • Journal Title

      J.Math.Anal.Appl. 335

      Pages: 298-313

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the unqueness of solutions with prescribed numbers of zeros for a two-point boundary value problem2007

    • Author(s)
      Satoshi Tanaka
    • Journal Title

      Differential and Integral Equations 20

      Pages: 93-104

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Decomposition of phase space for linear Volterra difference equations in a Banach space2006

    • Author(s)
      Yutaka Nagabuchi
    • Journal Title

      Funkcial. Ekvac. 49

      Pages: 269-290

    • NAID

      130000140668

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Decomposition of phase space for linear Volterra difference equations in a Banach space2006

    • Author(s)
      Yutaka Nagabuchi
    • Journal Title

      Funkcial.Ekvac. 49

      Pages: 269-290

    • NAID

      130000140668

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On global asymptotic stability of nonlinear stochastic difference equation with delays2006

    • Author(s)
      Yoshihiro Hamaya
    • Journal Title

      International Journal of Difference Equation 1・1

      Pages: 101-118

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Discreteness of subgroups of PU(1,2;C)2006

    • Author(s)
      Shigeyasu Kamiya
    • Journal Title

      Proceedings of the 9th International Conference on Real and Complex Analysis

      Pages: 48-55

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability properties of linear Volterra integrodifferential equations in a Banach space2005

    • Author(s)
      Yoshiyuki Hino
    • Journal Title

      Funkcial. Ekvac. 48

      Pages: 367-392

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of functional difference equations2005

    • Author(s)
      Hideaki Matsunaga
    • Journal Title

      Journal of Mathematical Analysis and Applications 305

      Pages: 391-410

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] Stability properties for linear Volterra difference equations with convolution kernels (関数方程式系と複雑系)2005

    • Author(s)
      Satoru Murakami
    • Journal Title

      数理解析研究所講究録 1445

      Pages: 143-153

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability properties and asymptotic almost periodicity for linear Volterra difference equations in a Banach space2005

    • Author(s)
      Satoru Murakami
    • Journal Title

      Japanese Journal of Mathematics 31

      Pages: 193-223

    • NAID

      10020427296

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilityproperties of linear Volterra integrodifferential equations in a Banach space2005

    • Author(s)
      Yoshiyuki Hino, Satoru Murakami
    • Journal Title

      Funkcial.Ekvac vol.48

      Pages: 367-392

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of solutions of functional difference equations2005

    • Author(s)
      Hideaki Matsunaga, Satoru Murakami
    • Journal Title

      J.Math.Anal.Appl. vol. 305

      Pages: 391-410

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Decomposition of phase space for linear Volterra difference equations in a Banach space2005

    • Author(s)
      Yutaka Nagabuchi
    • Journal Title

      Funkcial.Ekvac. vol.49

      Pages: 269-290

    • NAID

      130000140668

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability properties and asymptoticalmost periodicity for linear Volterra difference equations in a Banach space2005

    • Author(s)
      Satoru Murakami, Yutaka Nagabuchi
    • Journal Title

      Japanese J.Mathematics vol.31

      Pages: 193-223

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability properties of linear Volterra integrodifferential equations on a Banach space2005

    • Author(s)
      Yoshiyuki Hino
    • Journal Title

      Funkcial.Ekvac. 48

      Pages: 367-392

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stability properties and asymptotic almost periodicity for linear Volterra difference equations in a Banach space2005

    • Author(s)
      Satoru Murakami
    • Journal Title

      Japanese Journal of Mathematics 31・2

      Pages: 193-223

    • NAID

      10020427296

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stability properties for linear Volterra difference equations with convolution kernels in a Banach space(関数方程式と複雑系)2005

    • Author(s)
      Satoru Murakami
    • Journal Title

      数理解析研究所講究録 1445

      Pages: 143-153

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Discrete subgroups of PU(1.2;C) with parabolic elements2005

    • Author(s)
      Shigeyasu Kamiya
    • Journal Title

      Proceedings of the 12th International Conference on Finite or Infinite Dimensional Complex Analysis

      Pages: 155-162

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Massera's theorems for almost periodic solutions of functional differential equations2004

    • Author(s)
      Satoru Murakami
    • Journal Title

      Journal of Mathematical Society of Japan 56・1

      Pages: 247-268

    • NAID

      10013122753

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      Tetsuo Furumochi
    • Journal Title

      Japanese Journal of Mathematics 30・2

      Pages: 387-412

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A generalization of Wiener's lemma and its application to Volt erra difference equations on a Banach space2004

    • Author(s)
      Tetsuo Furumochi
    • Journal Title

      Journal of Difference Equations and Applications 10

      Pages: 1201-1214

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some invariant manifolds for functional difference equations with infinite delay2004

    • Author(s)
      Hideaki Matsunaga
    • Journal Title

      Journal of Difference Equations and Applications 10

      Pages: 661-689

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Massera's theorem for almost periodic solutions of functional differential equations2004

    • Author(s)
      Satoru Murakami, Toshiki Naito, Nguyen V. Minh
    • Journal Title

      J.Math.Soc.Japan vol.56

      Pages: 247-268

    • NAID

      10013122753

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      Tetsuo Furumochi, Satoru Murakami, Yutaka Nagabuchi
    • Journal Title

      Japanese J.Mathematics vol.30

      Pages: 387-412

    • NAID

      10014334745

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space2004

    • Author(s)
      Tetsuo Furumochi, Satoru Murakami, Yutaka Nagabuchi
    • Journal Title

      J. Difference Appl. vol.10

      Pages: 1201-1214

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some invariant manifolds for functional difference equations with infinite delay2004

    • Author(s)
      Hideaki Matsunaga, Satoru Murakami
    • Journal Title

      J. Difference Appl. vol.10

      Pages: 661-689

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise delays2004

    • Author(s)
      Tetsuo Furumochi
    • Journal Title

      Japanese Journal of Mathematics 30・2

      Pages: 387-412

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space2004

    • Author(s)
      Tetsuo Furumochi
    • Journal Title

      Journal of Difference Equations and Applications 10

      Pages: 1201-1214

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Some invariant manifolds for functional difference equations with infinite delay2004

    • Author(s)
      Hideaki Matsunaga
    • Journal Title

      Journal of Difference Equations and Applications 10・7

      Pages: 661-689

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Invariant manifolds for abstract functional differential equations and related Volterra difference equations in a Banach space

    • Author(s)
      Satoru Murakami
    • Journal Title

      Funkcial. Ekvac. (印刷中)

    • NAID

      130000140684

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Characterization of linear integral equations with nonnegative kernels

    • Author(s)
      Toshiki Naito
    • Journal Title

      J. Math. Anal. Appl. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the uniqueness of solutions with prescribed numbers of zeros for a two-point boundary value problem

    • Author(s)
      Satoshi Tanaka
    • Journal Title

      Differential and Integral Equations (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Invariant manifolds for abstract functional differential equations and related Volterra difference equations in a Banach space

    • Author(s)
      Satoru Murakami, Yutaka Nagabuchi
    • Journal Title

      Funkcial. Ekvac. (in press)

    • NAID

      130000140684

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Characterization of linear integral equations with nonnegative kernels

    • Author(s)
      Toshiki Naito, J.S.Shin, Satoru Murakami, Pham A.Ngoc
    • Journal Title

      J. Math.Anal.Appl. (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the uniqueness of solutions with prescribed numbers of zeros for a two-point boundary value problem

    • Author(s)
      Satoshi Tanaka
    • Journal Title

      Differential and Integral Equations (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability properties of linear Volterra integrodifferential equations on a Banach space

    • Author(s)
      Yoshiyuki Hino
    • Journal Title

      Funkcial.Ekvac. (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stability properties and asymptotic almost periodicity for linear Volterra difference equations in Banach pace

    • Author(s)
      Satoru Murakami
    • Journal Title

      Japanese Journal of Mathematics (発表予定)

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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