| Project/Area Number |
63540119
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Osaka University |
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Principal Investigator |
YAMAMOTO Minoru Osaka University, Mathematical Sciences, Professor, 工学部, 教授 (50029419)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Seiji Osaka University, Mathematical Sciences, Research Assistant, 工学部, 助手 (90225714)
MOHRI Masayuki Osaka University, Mathematical Sciences, Research Assistant, 工学部, 助手 (80127307)
MARUO Kenji Osaka University, Mathematical Sciences, Assictant Professor, 工学部, 講師 (90028225)
OHNAKA Kohzaburo Osaka University, Mathematical Sciences, Associate Professor, 工学部, 助教授 (60127199)
都田 艶子 大阪大学, 工学部, 教務職員 (80174150)
坂田 定久 大阪電気通信大学, 助教授 (60175362)
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| Project Period (FY) |
1988 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1990: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1988: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | Ordinary Differential Equations / Stability / Asymptotic Behavior / Periodisity / Boundary Value Problems / Oscillation / Liaqunov's Method / Fixed Point Theorems / 常微分方程式系 / 安定性 / 漸近的性質 / 周期解 / 境界値問題 / 解の振動性 / リヤプノフの方法 / 不動点定理 / 常微分方程式 / 解の一意性 / 漸近性 / 振動性 |
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| Research Abstract |
Stability therorems obtained in articles by Murakami-Yamamoto [3] [13], Wada-Yamamoto [4] [11], Saito-Yamamoto [6] [10], and Ohe-yamamoto [7] [15] are extensitions of many results.
Oscillation theorems for second order nonlinear differential equations by Nagabuchi-Yamamoto [2] are extensions of those obtained by yan in 1986.
On the existence of periodic solutions of nonlinear systems are considered in Saito-Yamamoto [5] and Sugie-Yamamoto [14] and had new results.
Uniqueness theorems of periodic solutions of Lineard equations are proved in Hirano-Yamamoto [1] [12].
Existence theorems of solutions for quasilinear systems are proved in Saito-Yamamoto [8] [9].
Continuous dependence of periodic solutions for periodic systems are discussed in Saito-Yamamoto [16] and obtained extensions of the theorems due to Cronin, Hale and Mawhin respectively.
All results above are extensions of those obtained by many authors. Throughout the above articles, it can be considered that almost all of our purpose had been achieved.
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