二阶变系数微分方程组解的有界性与渐近性

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The Boundedness and Asymptotic Behavior of Solutions of Differential System of Second-Order with Variable Coefficients

摘要: 已知微分方程组现研究它解的有界性与渐近性.当(0.1)的系数 P_ij(t)是周期函数时, Бурдика^[1]曾加以研究,而当P_ij(t)是任意函数时,至今还未曾有人研究过.此外, 所用的方法,只适用于周期系数的情况,对于一般情况并不适用.在本文中,我们将给出一种研究方法,它既适用于周期系数的情况,也适用于一般情况.

Abstract: In this paper, the differential system of second-order with variable coefficients is studied, and some criteria of the boundedness and asymptotic behavior for solutions are given.Consider a system of differential equations (0.1) Now we study the boundedness and asymptotic behavior of its solutions. In the case of P_if(t) being periodic functions, it was investigated by Burdina; in the case of P_if(t) being arbitrary functions, it has not been investigated yet. Besides, the method used by Burdina is only appropriate for the former but not for the latter case. In this paper we shall give a method which is appropriate for both cases.

[1]	Бурдика,В,N.,Критерий ограниченностм решений системы диффсрецинлъных уравнения 2-го порядка с периодическими коеффиуенмами.ДАН.СССР,новая серия,(1953)Том ХС No3
[2]	Borg G.,On a Liapouaoff criterioa of stability,Amer,Journ,of Math,71,(1949)
[3]	Сонсоне(Sапsопе.G),Обыкноэенные бцфференццалъные ураененця Том Ⅱ,(1954)