Periodic solutions of impulsive differential equations with piecewise alternately advanced and retarded argument of generalized type
Kuo‐Shou Chiu
Abstract
We investigate the existence of the periodic solutions of a quasilinear impulsive differential equation with alternately advanced and retarded arguments of generalized type, in short IDEPCAG. By using some fixed point theorems and some new analysis techniques, sufficient conditions are obtained for the existence and uniqueness of periodic solutions of these IDEPCAG systems. A new IDEPCAG’s Gronwall-type lemma is proved. Some examples concerning impulsive biological models such as Lasota–Ważewska model, Nicholson’s blowflies and logistic models are treated.
Topics & Concepts
MathematicsUniquenessLemma (botany)PiecewiseType (biology)Mathematical analysisDifferential equationOrdinary differential equationFixed-point theoremApplied mathematicsPoaceaeEcologyBiologyMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods