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We study the Tricomi problem for equations of mixed type with multiple functional delay and advance. A general solution of the equations is obtained. The problem is uniquely solvable. [ABSTRACT FROM AUTHOR]

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]

This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations in question. [ABSTRACT FROM AUTHOR]

We establish certain sufficient conditions guaranteeing the boundedness of all solutions of some third-order delay differential equations. [ABSTRACT FROM AUTHOR]