Liu, Yuji Anti-periodic solutions of nonlinear first order impulsive functional differential equations. (English) Zbl 1274.34229 Math. Slovaca 62, No. 4, 695-720 (2012). Summary: The existence of anti-periodic solutions of the following nonlinear impulsive functional differential equation \[ x'(t)+a(t)x(t)=f\Bigl (t,x(t),x\bigl (\alpha _1(t)\bigr), \ldots ,x\bigl (\alpha _n(t)\bigr)\Bigr), \qquad t\in \mathbb R, \]\[ \Delta x(t_k)=I_k\bigl (x(t_k)\bigr), \qquad k\in \mathbb Z \] is studied. Sufficient conditions for the existence of at least one anti-periodic solution are established. Several new existence results are obtained. Cited in 2 Documents MSC: 34K45 Functional-differential equations with impulses 34K13 Periodic solutions to functional-differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:anti-periodic solution; impulsive functional differential equation; fixed-point theorem; growth condition PDFBibTeX XMLCite \textit{Y. Liu}, Math. Slovaca 62, No. 4, 695--720 (2012; Zbl 1274.34229) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.