具有奇性的时滞Rayleigh方程周期正解存在性

Periodic Solutions of Rayleigh Equation with a Singularity and a Deviating Argument

研究了含有奇性的时滞Rayleigh方程x″(t)+f(x'(t))+g(t,x(t-σ))=0周期正解的存在性问题,其中f:R→R连续,g:R×(0,∞)→R连续,关于t为T周期,且在x=0处具有奇性,即limx→0+g(t,x)=∞.利用Mawhin重合度延拓定理,证明了上述方程至少存在一个T周期正解.

By using Mawhin＇s continuation theorem,the existence of periodic solutions for the Rayleigh equation with a singularity and a deviating argument x″（ t） ＋ f（ x＇（ t）） ＋ g（ t,x（ t- σ）） = 0 were studied,where f： R→R,g： R ×（ 0,∞） →R were continuous. It was proved that the above equation had at least one T-periodic positive solution,limx→0＋ g（ t,x） = ∞.