高速机构中的泛函微分方程研究

THE STUDY ON FUNCTIONAL DIFFERENTIAL EQUATIONS IN HIGH SPEED MECHANISMS

考虑在高速机构中有着广泛应用的二阶泛函微分方程(r(t)x′(t))′+a(t)x^a(t-τ(t))=f(t).(A)其中0<a<1,是两个奇数之比.文中给出了保证方程(A)的一切振动解渐近趋于零的若干充分条件.

In this paper we consider the functional differential equations of second order where 0<α<1 and a is a ratio of odd integers. The equations have extensive applications to high speed mechanisms. Several sufficient conditions have been found to ensure that all oscillatory solutions of (A) approach zero asymptotically.