Rayleigh型时滞平均曲率方程的周期解问题

Periodic solutions for a kind of prescribed mean curvature Rayleigh equation with a deviating argument

摘要:

本文讨论了一类Rayleigh型时滞平均曲率方程 并应用Mawhin重合度扩展定理我们证明了此方程至少存在一个T-周期解。

关键词:周期解;扩展定理;Rayleigh平均曲率方程

Abstract:

In this paper, the prescribed mean curvature Rayleigh equation with a deviating argument $$(\frac{u'(t)}{\sqrt{1+(u'(t))^2}})'+f(t,u'(t))+g(u(t-\tau(t)))=p(t)$$ is studied,and we prove that the given equation has at least one $T-$periodic solutions by using Mawhin's continuation theorem.

Key words:Periodic solutions; Continuation theorem; Prescribed mean curvature Rayleigh equation