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Existence of Almost periodic solutions for functional differential equation

Research Project

Project/Area Number 14540152
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionChiba University

Principal Investigator

HINO Yoshiyuki  Chiba University, Faculty of Science, Professor, 理学部, 教授 (70004405)

Co-Investigator(Kenkyū-buntansha) OKADA Yasunoti  Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (60224028)
ISHIMURA Ryuichi  Chiba University, Faculty of Science, Professor, 理学部, 教授 (10127970)
INABA Takashi  Chiba University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (40125901)
MURAKAMI Satoru  Univ.of Okayama Science, Professor, 理学部, 教授 (40123963)
NAITO Toshiki  Univ.of Electronics and Informatics, Professor, 電気通信学部, 教授 (60004446)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywordsfunctional differential equations / almost periodic solution / periodic solution / Bohr Spectrum / constant formula / 安定性 / スペクトル
Research Abstract

If we consider an evolution equations which is a generalization of partial differential equations with infinite delay, The phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. In this report, we have the followings for the above equations :
(i)Phase space and decompositions.
(ii)Liapunov's method and existence theorems of almost periodic solutions.
(iii)existence theorem for linear systems.
(iv)existence of almost periodic solution for nonlinear systems.
In particular, existence theorems of almost periodic solutions and almost automorphic solutions are shown by using the constant formula. These are generalizations of Massera Type theorems for periodic systems. And, Bohr spectrum of the solutions are inherited from that of perturbed terms.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Y.Hino, S.Murakami: "Almost automorphic solutions for abstract FDE"J.Math.Anal.Appl.. 286. 741-752 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hino, S.Murakami, N.V.Ming: "Decomposition of variation of constants formula for abstract FDE"Funkcial.Ekvac.. 45. 341-372 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hino, S.Murakami, T.Naito, N.V.Minh: "A variation-of-constant-formula for abstract FDE in the phase space"J.differential Eqs.. 179. 336-355 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hino, S.Murakami: "Limiting equations and some stability properties for asymptotically almost periodic"Tohoku Math.J.. 54. 239-257 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hino, S.Murakami: "Total stability and the existence of ap integrals for ap general processes"Vietnam J.Math.. 30. 425-435 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Inaba: "Open Engel manifolds admitting compact characteristic leaves"Bull.Austral.Math.Sci.. 56. 213-219 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hino, T.Naito, N.V.Minh, J.S.Shin: "Almost Periodic Solutions of Differential Equations"Taylor and Fisher. 247 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yoshiyuki Hino, Satoru Murakami: "Almost automorphic solutions for abstract functional differential equations"J.Math.Anal.Appl. 286. 741-752 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yoshiyuki Hino, Satoru Murakami, N.V.Minh: "Decomposition of variation of constants formula for abstract functional differential equations"Funkcial.Ekvac.. 45. 341-372 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yoshiyuki Hino, Satoru Murakami: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Math.J.. 54. 239-257 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Inaba: "Open Engel manifolds admitting compact characteristic leaves"Bull.Austral.Math.Soc.. 68. 213-219 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuo Furumochi, Toshiki Naito, N.V.Minh: "Boundedness and almost periodicity of solutions of partial functional differential equations"J.Differential eqs.. 180. 125-152 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hino, S.Murakami: "Almost automorphic solutions for abstract functional differential equations"J.Math.Anal.Appl.. 286. 741-752 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hino, S.Murakami, N.V.Minh: "Decomposition of variation of constants formula for abstract functional differential equations"Funkcial.Ekvac.. 45. 341-372 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hino, S.Murakami, T.Naito, N.V.Minh: "A variation-of-constants formula for abstract functional differential equations in the phase space"J.Differential Eqs.. 179. 336-355 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hino, S.Murakami: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations"Tohoku Math.J.. 54. 239-257 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hino, S.Murakami: "Total stability and the existence of almost periodic integral for almost periodic general processes"Vietnam J.Math.. 30. 425-435 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Inaba: "Open Engel manifolds admitting compact characteristic leaves"Bull.Austral.Math.Sci.. 56. 213-219 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hino, T.Naito, N.V.Minh, J.S.Shin: "Almost Periodic Solutions of Differential Equations in Banach Space"Taylor and Fishers. 247 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hino, S.Murakami, N.V.Minh: "Decomposition of variation of constants formula for abstract functional differential equations"Funkcialaj Ekvacioj. 45. 341-372 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Hino, S.Murakami, T.Naito, N.V.Minh: "A variation-of-constants formula for abstract functional differential equations in the phase space"J. Differential Equations. 179. 336-355 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Hino, S.Murakami: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Mathematical Journal. 54. 239-257 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Naito, N.V.Minh, J.S.Shin, Y.Hamaya: "Boundedness and almost periodicity in dynamical systems"J. Differential Equations and Applications. 7・4. 507-527 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Hino, T.Naito, N.V.Minh, J.S.Shin: "Almost Periodic Solutions of Differential Equations in Banach space"Taylor and Fishers. 247 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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