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Positive periodic solutions for impulsive differential equations with infinite delay and applications to integro‐differential equations
Author(s) -
BuedoFernández Sebastián,
Faria Teresa
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6100
Subject(s) - mathematics , nonlinear system , delay differential equation , mathematical analysis , differential equation , scalar (mathematics) , c0 semigroup , fixed point theorem , geometry , quantum mechanics , physics
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.