1993 Fiscal Year Final Research Report Summary
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 Osaka University, Assistant Professor, 工学部, 講師 (90225714)
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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)
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| Project Period (FY) |
1991 – 1993
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| Keywords | Ordinary Differential Equations / Asymptotic Behavior / Periodicity / Stability / Oscillation / Fixed Point Theorems / Liapunov's Method / Invarince Principle |
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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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