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Asymptotic behaviors and oscillation of solutions for differential equation

微分方程解的渐近行为和振荡

基本信息

批准号：
03640152
负责人：
SAITO Seiji
金额：
$ 1.09万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1993
项目状态：
已结题

项目摘要

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.

利用不动点定理，在Saito-Yamamoto[1]中讨论了周期拟线性常微分方程周期解关于参数的连续依赖性，并分别得到了Cronin、Hale和Mahwin的定理的推广。Saito[2]讨论了常微分线性系统与拟线性系统的稳定性和渐近等价性，并用一些新方法改进了解的渐近行为定理。考虑二阶非线性常微分方程解的有界性和单调性，得到了Wong和Marini-Zezza的定理的推广。在Nagabuchi-Yamamoto[4]中，利用辅助函数和不变性原理，研究了一类具有连续项的广义Lienard方程解振动的一个新的充要条件。上述关于常微分方程解的渐近性态和振动性的结果是许多研究者所得到的结果的推广。纵观以上文章，可以认为我们几乎所有的目的都达到了。此外，在Ohnaka[5]和Ohnaka- oshiumi[6]中，对确定性分布参数系统的外力辨识方法进行了一些研究，并给出了数值算例来说明本文方法的适用性。在Miyakoda[7-9]中，我们讨论了复多项式方程的多零Durand-Kerner近似的局部性质。