一类二阶微分方程周期解的存在性

Existence of Periodic Solutions for a Class of Second Order Differential Equations

研究一类具有偏差变元的二阶微分方程x″(t)+f(x′(t))+h(x(t))x′(t)+g(t,x(t-τ(t)))=p(t)的周期解的存在性问题.通过应用Schwarz不等式,Minkowski不等式,以及重合度理论,在满足一定条件下,得到方程至少存在一个T-周期解的新结果,且其周期解存在性的充分条件并不要求h(x)是有界函数.

In this paper, we study the problem on the existence of periodic solutions for a class of second order differential equations with a deviating argument x＇＇（t） ＋f（x＇ （t）） ＋h （x（t））x＇ （t） ＋g（t, x（t-τ（t） ） ） = p（t）. By means of Schwarz＇ s inequality and Minkowski＇s inequality and the coincidence degree theory, a new result on the existence of periodic solutions for the equations is obtained under some conditions. In the sufficient conditions of the existence of periodic solutions for the equations, the bounded function h（x） may not be required.