Multiplicity Results on Period Solutions to Higher Dimensional Differential Equations with Multiple Delays.

This paper deals with the existence and multiplicity of periodic solutions to delay differential equations of the form where $${z\in {\bf R}^N, f\in C({\bf R}^{N}, {\bf R}^N)}$$. By using the S pseudo geometrical index theory in the critical point theory, some known results for Kaplan-Yorke type differential delay equations are generalized to higher dimensional case. As a result, the Kaplan-Yorke's conjecture is proved to be true in the case of higher dimensional systems. [ABSTRACT FROM AUTHOR]