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

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.