Infinitely Many Periodic Solutions to Delay Differential Equations via Critical Point Theory

Abstract

By the critical point theory, infinitely many 4σ-periodic solutions are obtained for the system of delay differential equations $ẋ\left(t\right)=-f(x(t-\sigma ))$, where $\sigma \in (0,+\infty )$ and $f\in C({ℝ}^n,{ℝ}^n)$. It is shown that all the periodic solutions derived here are brought about by the time delay.