具有变参数中立型Rayleigh方程周期解的存在性

Existence of Periodic Solutions for a Kind of Neutral Rayleigh Equation with Variable Parameters

利用重合度理论的连续性定理,研究一类可变参数中立型Rayleigh泛函微分方程(φp(x(t)-c(t)x(t-r))(k))(k)+∑mi=1αi(t)f(x’(t-μi(t)))+∑nj=1βi(t)g(x(t-τj(t)))=e(t).获得其周期解存在性新的充分条件,推广和改进了已有文献中的相关结论.

By using the continuation theorem of coincidence degree,this paper studies a kind of neutral Rayleigh functional differential equation with variable parameters(φp(x(t)-c(t)x(t-r))(k))(k)+∑mi=1αi(t)f(x’(t-μi(t)))+∑nj=1βi(t)g(x(t-τj(t)))=e(t).Some new sufficient conditions for the existence of periodic solutions are obtained.The results have extended and improved the relat-ed reports in the literature.