二阶滞后型微分方程解的性状以及强迫振动准则

The Oscillations and Properties of Solution of 2nd Order Delay Differential Equation

本文给出了二阶滞后型微分方程ｘ（ｔ）＋α（ｔ）ｘ（ｔ－τ）振动解与ａ（ｔ）的关系以及边值问题解与特征值的关系，同时给出了两类二阶滞后型微分方程的强迫振动准则，以及二阶滞后方程ｘ（ｔ）＋ｐ（ｔ）ｘ（ｔ）＋Ｎ（ｔ）ｘ（ｔ）Ｍ（ｔ）ｘ（ｔ－（△ｔ））＝０与常微分方程的关系。

Abstract This paper gives the coercive oscillation rules of two class 2nd delay differential equations, and the relations between the boundary ralue problem and characteristic value of the delay differential equation x(t)+a(t)x(t- )=0, between another delay differential equation x(t)+ p(t)x(t)+ N(t)x(t)+ M(t)x(t-△(t))= 0 and a ordinary differential equation.