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In this paper, we study the periodic solutions to a type of differential delay equations with two lags of ratio (2k−1)/2$(2k-1)/2$ in the form x′(t)=−f(x(t−2))−f(x(t−(2k−1))),k≥2.$$x'(t)=-f \bigl(x(t-2) \bigr)-f \bigl(x \bigl(t-(2k-1) \bigr) \bigr),\quad k\geq2. $$ The 4k-periodic solutions are obtained by using the variational method and the method of Kaplan-Yorke coupling system. This is a new type of differential-delay equations compared with all previous researches since the ratio of two lags is not an integer. Three functionals are constructed for a discussion on critical points. An example is given to demonstrate our main results.

Periodic orbits to Kaplan-Yorke like differential delay equations with two lags of ratio ( 2 k − 1 ) / 2 $(2k-1)/2$