Abstract
In this paper we consider a class of second-order neutral functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of Z_{2} group index theory and variational methods. The main result is also illustrated with an example.
Highlights
In this paper we consider a class of second-order neutral functional differential equations described by
The necessity to study delay differential equations is due to the fact that these equations are useful mathematical tools in modeling many real processes and phenomena studied in economics, biology, electronics, optimal control, mechanics, medicine, etc. [, ]
In recent years many researchers have focused on the existence of periodic solutions of delay differential equations; see, for example, [ – ]
Summary
In recent years many researchers have focused on the existence of periodic solutions of delay differential equations; see, for example, [ – ]. Several available approaches to tackle the existence of periodic solutions for delay differential equations include the dual Lyapunov method, the Fourier analysis method, fixed point theory, and the coincidence degree theory [ – ]. Some researchers have studied the existence of periodic solutions for delay differential equations via variational methods [ – ]. In [ ], Shu and Xu obtained the following result.
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