(en) A new definition of a guiding function for functional differential equations is given, which is sometimes better for applications than the known one by Mawhin. We then prove an existence result for periodic solutions of FDEs related to the new definition.
Fonda, A. (1987). Guiding Functions and Periodic-solutions To Functional-differential Equations. Proceedings of the American Mathematical Society, 99(1), 79-85. https://doi.org/10.1090/S0002-9939-1987-0866434-X (Original work published 1987)