Abstract
By the critical point theory, we study the existence and multiplicity of periodic solutions to the following system of delay differential equations: (*) x ′ ( t ) = - f ( x ( t - r ) ) , where x ∈ R n , f ∈ C ( R n , R n ) , and r > 0 is a given constant. A sufficient condition on the existence and multiplicity of periodic solutions for Eq. ( * ) is obtained. To the authors’ knowledge, this is the first time, the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly.
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