Project/Area Number 
13640197

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Basic analysis

Research Institution  Okayama University of Science 
Principal Investigator 
MURAKAMI Satoru Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (40123963)

CoInvestigator(Kenkyūbuntansha) 
TAKENAKA Shigeo Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (80022680)
YOSHIDA Kenichi Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (60028264)
HAMAYA Yoshihiro Okayama University of Science, Department of Information Science, Associated Professor, 総合情報学部, 助教授 (40228549)
SHIMENO Nobukazu Okayama University of Science, Department of Applied Mathematics, Associated Professor, 理学部, 助教授 (60254140)
KURIBAYASHI Katsuhiko Okayama University of Science, Department of Applied Mathematics, Associated Professor, 理学部, 助教授 (40249751)
中村 忠 岡山理科大学, 総合情報学部, 教授 (20069074)
渡辺 寿夫 岡山理科大学, 理学部, 教授 (40037677)

Project Period (FY) 
2001 – 2002

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2001: ¥1,800,000 (Direct Cost: ¥1,800,000)

Keywords  Functional differential equations / Fading memory space / Admissibility / Variationofconstants formula / Phase space / Solution operator / Quasiprocess / Stability property / 概周期解 / スペクトル / 線形化原理 / 関数微分方程 / 極限方程式 / プロセス / 差分方程式 / 遅れ時間 
Research Abstract 
Head investigator and 10 investigators studied qualitative properties for equations with time delay, and obtained many results on the subject. The contents of a part of results on the subject. The contents of a part of results obtained are summarized in the following: For an abstract functional differential equation which is the one of infinite dimension, we established a representation formula of solutions in the phase space, together with the decomposed formula. The formula plays an important role in the study of qualitive properties, because one can reduce the study of infinite dimensional equations to the study of finite dimensional equations by using the formula. Indeed, by applying the formula we established some results on the admissibility of some function spaces and Massera's type results on the existence of almost periodic solutions for linear functional differential equations. Also, we established some local invariant manifolds for nonlinear functional differential equations, and applied the results to some stability problems via linearized equations. Furthermore, for asymptotically almost periodic functional differential equations we studied the existence of asymptotically almost periodic solutions by means of limiting equations.
