Buedo-Fernández, Sebastián; Faria, Teresa Positive periodic solutions for impulsive differential equations with infinite delay and applications to integro-differential equations. (English) Zbl 1451.34089 Math. Methods Appl. Sci. 43, No. 6, 3052-3075 (2020). Summary: Sufficient conditions for the existence of at least one positive periodic solution are established for a family of scalar periodic differential equations with infinite delay and nonlinear impulses. Our criteria, obtained by applying a fixed-point argument to an original operator constructed here, allow to treat equations incorporating a rather general nonlinearity and impulses whose signs may vary. Applications to some classes of Volterra integro-differential equations with unbounded or periodic delay and nonlinear impulses are given, extending and improving results in the literature. Cited in 1 Document MSC: 34K13 Periodic solutions to functional-differential equations 34K45 Functional-differential equations with impulses 45J05 Integro-ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:delay differential equations; fixed-point theorems in cones; impulses; infinite delay; positive periodic solution; Volterra integro-differential equations PDFBibTeX XMLCite \textit{S. Buedo-Fernández} and \textit{T. Faria}, Math. Methods Appl. Sci. 43, No. 6, 3052--3075 (2020; Zbl 1451.34089) Full Text: DOI