The author obtains some results on the existence, nonexistence and multiplicity of positive periodic solutions for a family of functional periodic differential equations of second order of the form
The main tool used is the Krasnoselkii fixed point theorem in cones. For closely related results, see, e.g. [H. Y. Wang, J. Differ. Equations 202, No. 2, 354–366 (2004; Zbl 1064.34052)], [Y. Wu, Nonlinear Anal., Theory Methods Appl. 68, No. 7(A), 1954–1962 (2008; Zbl 1146.34049)].