Periodic Solutions for a Prescribed Mean Curvature Equation with Multiple Delays

Abstract

We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation $(d/dt)(x\mathrm{\text{'}}(t)/\sqrt{1+{\left(x\mathrm{\text{'}}\left(t\right)\right)}^2})\mathrm{ }+{\sum }_{i=1}^n{a}_i\left(t\right)g\left(x\left(t-{\tau }_i\left(t\right)\right)\right)=p\left(t\right)$. By using Mawhin's continuation theorem, a new result is obtained. Furthermore, the nonexistence of periodic solution for the equation is investigated as well.