Favard's theorem of piecewise continuous almost periodic functions and its application

In this paper, by constructing Bochner-Fejer polynomials for piecewise continuous almost periodic functions (PCAP, for short), the authors establish Favard's theorem of PCAP functions, which illustrates when the primitive function of PCAP function is a PCAP function. As its application, combining coincidence degree theory, we consider the existence of PCAP solution of impulsive single population model with hereditary effects. To our best knowledge, it is the first time when coincidence degree theory is used to study the existence of PCAP solution of impulsive differential equation. (C) 2013 Elsevier Inc. All rights reserved.