具多偏差变元的高阶中立型Rayleigh方程周期解的存在性

Existence of Periodic Solutions for a Class of High Order Neutral Functional Differential Equation with Multiple Deviating Arguments

利用Mawhin重合度拓展定理,获得了一类具偏差变元的高阶中立型Rayleigh方程(x(t)-(?)c_lx(t-r_l))^(k)+(?)α_i(t)f(x′(t-μ_i(t)))+(?)β_j(t)g(x(t-τ_j(t)))=p(t)周期解存在性的充分条件,推广和改进了已有文献的相关结果.

In this paper, by employing Mawhin＇s continuation theorem, some new sufficient condition of the existence of periodic solutions for a kind of high-order Neutral functional differential equation with multiple deviating arguments shch as （x（t）-∑l=1^q clx（t-τ1））^（k）＋∑i=1^m αi（t）f（x′（t-μi（t）））＋∑j=1^nβj（t）g（x（t-τj（t）））=p（t） The results have been extend and improved the related reports in the literatures.