Asymptotic behaviors and oscillation of solutions for differential equation
| Project/Area Number |
03640152
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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 |
SAITO Seiji (1993) Osaka University, Assistant Professor, 工学部, 講師 (90225714)
山本 稔 (1991-1992) 大阪大学, 工学部, 教授 (50029419)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAKODA Tsuyako Osaka University, Research Assistant, 工学部, 教務員 (80174150)
NAGABUCHI Yutaka Osaka University, Research Assistant, 工学部, 助手 (60252607)
OHNAKA Kohzaburo Osaka University, Associate Professor, 工学部, 助教授 (60127199)
斎藤 誠慈 (齋藤 誠慈) 大阪大学, 工学部, 講師 (90225714)
丸尾 健二 大阪大学, 工学部, 講師 (90028225)
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| Project Period (FY) |
1991 – 1993
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| Project Status |
Completed (Fiscal Year 1993)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1991: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Ordinary Differential Equations / Asymptotic Behavior / Periodicity / Stability / Oscillation / Fixed Point Theorems / Liapunov's Method / Invarince Principle / Ordinary Differential / Stability Equations / 常微分方程式系 / 漸近的性質 / 安定性 / リエナール方程式 / 振動論 / 周期解 / 非線形関数解析学 / 不動点定理 / リエナ-ル方程式 |
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| Research Abstract |
Continuous dependence of periodic solutions concerning a parameter for periodic quasilinear ordinary diffrential equations is dealt with in Saito-Yamamoto [1] via fixed points theorems, and we obtain extensions of theorems due to Cronin, Hale and Mahwin respectively.
Saito [2] discusses stability and asymptotic equivalence of between ordinary differential linear systems and quasilinear systems, and has improved theorems of asymptotic behaviors of solutions by some new method.
Nagabuchi-Yamamoto [3] consider boundedness and monotonicity of solutions for second-order nonlinear ordinary differential equations and obtain some extensions of theorems due to Wong and Marini-Zezza.
In Nagabuchi-Yamamoto [4] a new necessary and sufficient condition for solutions of generalized Lienard equations with pertubing terms to oscillate is investigated by applying using auxiliary functions and the invariance principle.
The above results of asymptotic behaviors and oscillation of solutions for ordinary differential equations are extensions of those obtained by many investigators. Throughout the above articles, it can be considered that almost all of our purposes have been acheved.
Moreover in Ohnaka [5] and Ohnaka-Oshiumi [6] some studies on an identification method of external forces for a deterministic distributed-parameter system are obtained and numerical example are given for illustrating the applicability of our method.
And in Miyakoda [7-9] we discuss local properties of the Durand-Kerner approximation to multiple zeroes of complex polynomial equations.
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Report
(4 results)
Research Products
(39 results)
