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 ẋt=-f(x(t-σ)), where σ∈(0,+∞) and f∈C(ℝn,ℝn). It is shown that all the periodic solutions derived here are brought about by the time delay.