一类二阶非线性时滞微分方程周期解存在问题

Existence of Periodic Solutions to a Class of Nonlinear Second-Order Differential Equations with Delays

利用Mawhin重合度理论及一些分析技巧研究了二阶非线性时滞微分方程的周期解存在的问题:x″(t)+f(t,xt)[x'(t)]n+a(t)x3(t)+b(t)x2(t)+c(t)x(t)=p(t)(n>2);并给出方程至少存在3个周期性解的充分性定理.

By using the coincidence degree theory of Mawhin and some analytical skills, this paper studies the existence of periodic solutions to a class of nonlinear second order differential equations with delays as follows,：x″（t）＋f（t,xt）[x＇（t）]n＋a（t）x3（t）＋b（t）x2（t）＋c（t）x（t）=p（t）（n〉2）;some sufficient theorems for the existence of at least three periodic solutions to this equation are given.