Asymptotic behaviors and oscillation of solutions for differential equation

Saito-Yamamoto [1]利用不动点定理研究了周期拟线性常微分方程周期解对参数的连续依赖性，推广了Cronin，黑尔和Mahwin的不动点定理.Saito [2]讨论了常微分线性系统和拟线性系统的稳定性和渐近等价性，Nagabuchi-Yamamoto [3]考虑了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的一些定理的推广，Nagabuchi-Yamamoto [4]中的一些结果利用辅助函数和不变性原理，研究了一类带管项的广义Lienard方程解振动的一个新的充要条件.上述常微分方程解的渐近性态和振动性的结果推广了已有的结果.在上述文章中，Ohnaka [5]和Ohnaka-Oshiumi [6]对确定性分布参数系统的外力识别方法进行了研究，并给出了数值例子说明了方法的适用性; Miyakoda [7-9]讨论了Durand-复多项式方程多重零点的Kerner逼近。

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.