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2000 Fiscal Year Final Research Report Summary

QUALITATTVE STUDY OF SOLUTIONS OF FUNCTIONAL EQUATIONS AND ITS APPLICATIONS

Research Project

Project/Area Number 10440047
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionSHIMANE UNIVERSITY

Principal Investigator

FURUMOCHI Tetsuo  SHIMANE UNIVERSITY, Fac. Sci & Eng., PROFESSOR, 総合理工学部, 教授 (40039128)

Co-Investigator(Kenkyū-buntansha) NAITO Toshiki  THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, MATHEMATICS, PROFESSOR, 電気通信学部, 教授 (60004446)
KAMINOGO Takashi  TOHOKU GAKUIN UNIVERSITY, MATHEMATICS, PROFESSOR, 教養学部, 教授 (60124567)
HINO Yoshiyuki  CHIBA UNIVERSITY, MATHEMATICS, PROFESSOR, 理学部, 教授 (70004405)
MURAKAMI Satoru  OKAYAMA UNIVERSITY OF SCIENCE, MATHEMATICS, PROFESSOR, 理学部, 教授 (40123963)
SUGIE Jitsuro  SHIMANE UNIVERSITY, MATHEMATICS, PROFESSOR, 総合理工学部, 教授 (40196720)
Project Period (FY) 1998 – 2000
KeywordsPeriodic / almost periodic solutions / Stability / boundedness / oscillation / Fixed point theorem / Quasi-process / Solution curve / Spectrum / Mathematical biology model / Functional differential equations
Research Abstract

Many results concerning qualitative properties of solutions of functional equations were obtained by the head investigator and the investigators.
The head investigator obtained results concerning periodic solutions of neutral integral / integro-differential equations, stability and boundedness of solutions of Volterra integro-differential / differential equations, applications of fixed point theorems to the theory of stability, and almost periodic solutions of abstract functional differential equations.
Next, the first investigator obtained results concerning stability of solutions of quasi-processes, almost periodic solutions of almost periodic quasi-processes, and almost periodic solutions of abstract functional differential equations.
Similarly, the second investigator obtained results concerning structures of solution curves of functional differential equations.
Moreover, the third investigator obtained results concerning solution semigroups of linear functional differential equations, … More and applications of spectrum theory to the existence problems of periodic and almost periodic solutions.
On the other hand, the fourth investigator obtained results concerning mathematical biology models, the uniqueness of limit cycles, and oscillation of solutions of nonlinear differential equations.
Finally, the fifth investigator obtained results concerning stability of solutions of linear Volterra difference equations, spectral analysis of solutions of functional equations, and a variation-of-constants formula for abstract functional differential equations.
In addition to the above studies, the head investigator invited Professor T.A.Burton (one of the best rsearchers of functional equations in the world) from USA to Japan twice in 1999 and 2000, and received comments for the orientation and the summing up of the study, and reviews for the study. Moreover, the head investigator and investigators were invited to the international conferences held in Chengdu (China), Akdeniz (Turkey), Szeged (Hungary), Newport Beach (USA), Washington D.C.(USA), and Catania (Italy), and gave lectures concerning the obtained results in order to receive reviews for them. Less

  • Research Products

    (82 results)

All Other

All Publications (82 results)

  • [Publications] T.A.Burton: "Periodic solutions of a neutral integro-differential equation"Funkcialaj Ekvacioj. 41. 327-336 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Furumochi: "Stability and boundedness in Volterra integro-differential equations"Mem.Fac.Sci.and Eng.,Shimane Univ.. 32. 25-40 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.A.Burton: "Periodic and asymptotically periodic solutions of neutral integral equations"Electronic Journal of Qualitative Theory of Differential Equations. 10. 1-22 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Furumochi: "Periodic solutions of an integral equation"Stability and Control. 10. 203-210 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.A.Burton: "Existence theorems and periodic solutions of neutral integral equations"Nonlinear Analysis. 43. 527-546 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.A.Burton: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.A.Burton: "Krasnoselskii's fixed point theorem and stability"Nonlinear Analysis. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Furumochi: "Periodic solutions of Volterra difference equations and attractivity"Nonlinear Analysis. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Furumochi: "Boundedness and almost periodicity of solutions of partial functional differential equations"Journal of Differential Equations. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.A.Burton: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "Almost periodic processes and the existence of almost periodic solutions"Electronic Journal of Qualitative Theory of Differential Equations. 1. 1-19 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "A generalization of processes and stabilities in abstract functional differential equations"Funkcialaj Ekvacioj. 41. 235-255 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "Skew product flows of quasi-processes and stabilities"Fields Institute Communications. 21. 329-341 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "Total stability in abstract functional differential equations with infinite delay"Electronic Journal of Qualitative Theory of Differential Equations. 13. 1-9 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "A variation-of-constants formula for abstract functional differential equations in the phase space"Journal of Differential Equations. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Mathematical Journal. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiyuki Hino: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Kaminogo: "Kneser families in infinite-dimensional spaces"Nonlinear Analysis. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "The generator of the solution semigroup for the general linear functional differential equations"Bull.of the University of Electro-Communications. 11・1. 29-38 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations"Journal of Differential Equations. 152. 358-376 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jong Son Shin: "Semi-Fredholm operators and periodic solutions for linear functional differential equations"Journal of Differential Equations. 153. 407-441 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jong Son Shin: "Existence and continuous dependence of mild solutions to semilinear functional differential equations in Banach spaces"Tohoku Mathematical Journal. 51. 555-583 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "On a spectral criterion for almost periodicity of solutions to periodic evolution equations"Journal of Differential Equations. 1. 1-28 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jong Son Shin: "On stability of solutions in linear autonomous functional differential equations"Funkcialaj Ekvacioj. 43. 323-337 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "On the spectrum of some functional differential equations"Progress in Nonlinear Differential Equations and Their Applications. 42. 222-228 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "A decomposition theorem and the existence of periodic solutions of periodic differential equations"Journal of Differential Equations. 160. 263-282 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "Periodic and almost periodic solutions of functional differential equations with infinite delay"Nonlinear Analysis. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiki Naito: "New spectral criteria for almost periodic solutions of evolution equations"Studia Mathematica. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Two-parameter bifurcation in a predatoe-prey system of Ivlev type"J.Math Anal.Appl.. 217. 349-371 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "On global asymptotic stability of systems of Lienard type"J.Math.Anal.Appl.. 219. 140-164 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling type function response"Quarterly of Applied Mathematics. 58. 577-590 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Mathematical Journal. 7. 577-584 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Oscillation criteria for second order nonlinear differential equations of Euler type"J.Math Anal.Appl.. 253. 414-439 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"J.Bull.London Math.Soc.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Nonlinear oscillation problems for second order differential equation of Euler type"Nonlinear Analysis. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Jitsuro Sugie: "Lenard dynamics with an open orbit"Nonlinear Differential Equations Appl.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Saber Elaydi: "Uniform asymptotic stability in Volterra difference equations"J.Difference Equations and Appl.. 3. 203-218 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Saber Elaydi: "Asymptotic equivalence for difference equations with infinite delay"J.Difference Equations and Appl.. 5. 1-23 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Satoru Murakami: "Evolution semigroups and sums of commuting operators : a new approach to the admissibility theory of function spaces"Journal of Differential Equations. 164. 240-285 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Satoru Murakami: "Spectral analysis of an operator associated with linear functional differential equations and its applications"Electronic Journal of Qualitative Theory of Differential Equations. 20. 1-15 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.A.Burton and Tetsuo Furumochi: "Periodic solutions of a neutral integro-differential equation"Funkcialaj Ekvacioj. 41. 327-336 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Furumochi and Satoshi Matsuoka: "Stability and boundedness in Volterra integro-differential equations"Mem. Fac. Sci. and Eng., Shimane Univ.. 32. 25-40 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.A.Burton and Tetsuo Furumochi: "Periodic and asymptotically periodic solutions of neutral integral equations"Electronic Journal of Qualitative Theory of Differential Equations. 10. 1-22 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Furumochi: "Periodic solutions of an integral equation"Stability and Control. 10. 203-210 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.A.Burton and Tetsuo Furumochi: "Existence theorems and periodic solutions of neutral integral equations"Nonlinear Analysis. 43. 527-546 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.A.Burton and Tetsuo Furumochi: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.A.Burton and Tetsuo Furumochi: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.A.Burton and Tetsuo Furumochi: "Krasnoselskii's fixed point theorem and stability"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Furumochi, Toshiki Naito and Nguyen Van Minh: "Boundedness and almost periodicity of solutions of partial functional differential equations"J.Differential Equations. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Furumochi: "Periodic solutions of Volterra difference equations and attractivity"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino and Satoru Murakami: "A generalization of processes and stabilities in abstract functional differential equations"Funkcialaj Ekvacioj. 41. 235-255 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino and Satoru Murakami: "Almost periodic processes and the existence of almost periodic solutions"Electronic Journal of Qualitative Theory of Differential Equations. 1. 1-19 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino and Satoru Murakami: "Skew product flows of quasi-processes and stabilities"Fields Institute Communications. 21. 329-341 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino and Satoru Murakami: "Total stability in abstract functional differential equations with infinite delay"Electronic Journal of Qualitative Theory of Differential Equations. 13. 1-9 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino and Satoru Murakami: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino, Satoru Murakami, Toshiki Naito and Nguyen Van Minh: "A variation-of-constants formula for abstract functional equations in the phase space"J.Differential Equations. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiyuki Hino and Satoru Murakami: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Mathematical Journal. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Kaminogo: "Kneser families in infinite-dimensional spaces"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito, Jong Son Shin and Satoru Murakami: "The generator of the solution semigroup for the general linear functional differential equation"Bull. of the University of Electro-Communications. 11(1). 29-38 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito and Nguyen Van Minh: "Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations"J.Differential Equations. 152. 358-376 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jong Son Shin and Toshiki Naito: "Semi-Fredholm operators and periodic solutions for linear functional differential equations"J.Differential Equations. 153. 407-441 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jong Son Shin and Toshiki Naito: "Existence and continuous dependence of mild solutions to semilinear functional differential equations in Banach spaces"Tohoku Mathematical Journal. 51. 555-583 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito, Nguyen Van Minh, Rinko Miyazaki and Jong Son Shin: "A decomposition theorem and the existence of periodic solutions of periodic differential equations"J.Differential Equations. 160. 263-282 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jong Son Shin, Toshiki Naito and Nguyen Van Minh: "On stability of solutions in linear autonomous functional differential equations"Funkcialaj Ekvacioj. 43. 323-337 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito, Nguyen Van Minh and Jong Son Shin: "On the spectrum of some functional differential equations differential equations"Progress in Nonlinear Differential Equations and Their Applications.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito, Nguyen Van Minh and Jong Son Shin: "On the spectrum of some functional differential equations"Progress in Nonlinear Differential Equations and Their Applications. 42. 222-228 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito, Nguyen Van Minh and Jong Son Shin: "New spectral criteria for almost periodic solutions of evolution equations"Studia Mathematica. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiki Naito, Nguyen Van Minh and Jong Son Shin: "Periodic and almost periodic solutions of functional differential equations with infinite delay"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie: "Two-parameter bifurcation in a predator-prey system of Ivlev type"J.Math. Anal. Appl.. 217. 349-371 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie, D.-L.Chen and Hideaki Matsunaga: "On global asymptotic stability of systems of Lienard type"J.Math. Anal. Appl.. 219. 140-164 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie and Masaki Katayama: "Global asymptotic stability of a predator-prey system of Holling type"Nonlinear Analysis. 38. 105-121 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie: "Uniqueness of limit cycles in a predator-prey system of Holling type function response"Quarterly of Applied Mathematics. 58. 577-590 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie and Mitsuru Iwasaki: "Oscillation of the Riemann-Weber version of Euler differential equations with delay"Georgian Mathematical Journal. 7. 577-584 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitusro Sugie and Kazuhisa Kita: "Oscillation criteria for second order nonlinear differential equations of Euler type"J.Math. Anal. Appl.. 253. 414-439 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie: "Lienard dynamics with an open orbit"Nonlinear Differential Equations Appl.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie: "A nonoscillation theorem for second order nonlinear differential equations with decaying coefficients"J.Bull. London Math.Soc.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Jitsuro Sugie: "Nonlinear oscillation problems for second order differential equation of Euler type"Nonlinear Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Saber Elaydi and Satoru Murakami: "Uniform asymptotic stability in Volterra difference equations"J.Difference Equations and Appl.. 3. 203-218 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Saber Elaydi, Satoru Murakami and Etsuyo Kamiyama: "Asymptotic equivalence for difference equations with infinite delay"J.Difference Equations and Appl.. 5. 1-23 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Satoru Murakami, Toshiki Naito and Nguyen Van Minh: "Spectral analysis of an operator associated with linear functional differential equations and its applications"Electronic Journal of Qualitative Theory of Differential Equations. 20. 1-15 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Satoru Murakami, Toshiki Naito and Nguyen Van Minh: "Evolution semigroups and sums of commuting operators : a new approach to the admissibility theory of function spaces"J.Differential Equations. 164. 240-285 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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