具偏差变元的一类三阶微分方程的周期解

Periodic Solutions for a Class of Third Order Differential Equations with Deviating Argument

利用Mawhin重合度理论,研究了具偏差变元的一类三阶微分方程x'''(t)+f(x(t),x(t-τ0(t)),x'(t-τ1(t)),x″(t-τ2(t)))=p(t)的周期解的问题.结合Schwarz不等式,运用分析的技巧对集合Ω的先验界作出准确的估计,得到周期解存在的新的结果.所得定理不仅依赖于f(x,y,z,w)而且依赖于偏差变元τ0(t),τ1(t)和τ2(t),并举例说明结果的有效性.

By employing the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions for third order differential equations with deviating argument x＇＇＇（t）＋f（x（t）,x（t-τ0（t））,x′（t-τ1（t））,x″（t-τ2（t）））=p（t）.Coupled with Schwarz inequality and technique of analysis,an estimation of prior bound of set Ω is given,then some new results on the existence of periodic solutions of the equations are obtained.Our theorems are related to f（x,y,z,w） as well as the deviating argument τ0（t）,τ1（t） and τ2（t）.Meanwhile,an example is given to illustrate the effect of our results.