Abstract
We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation(d/dt)(x'(t)/1+x't2) +∑i=1naitgxt-τit=pt. By using Mawhin's continuation theorem, a new result is obtained. Furthermore, the nonexistence of periodic solution for the equation is investigated as well.
Highlights
We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation (d/dt)(x(t)/√1 + (x (t))2) + ∑ni=1 ai (t) g (x (t − τi (t))) = p (t)
Prescribed mean curvature equation arises from some problems associated with differential geometry and physics such as combustible gas dynamics [1,2,3]
Considering the delay phenomenon which exists generally in nature, Feng [22] studied the existence of periodic solutions for the one-dimensional mean curvature type equation in the following form: d dt
Summary
Prescribed mean curvature equation arises from some problems associated with differential geometry and physics such as combustible gas dynamics [1,2,3]. We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation (d/dt)(x(t)/√1 + (x (t))2) + ∑ni=1 ai (t) g (x (t − τi (t))) = p (t). The nonexistence of periodic solution for the equation is investigated as well.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
