Instability of Rapidly-oscillating Periodic Solutions for Discontinuous Differential Delay Equations

Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay

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Global Continua of Rapidly Oscillating Periodic Solutions of State-Dependent Delay Differential Equations

We apply our recently developed global Hopf bifurcation theory to examine global continuation with respect to the parameter for periodic solutions of functional differential equationswith state-dependent delay.We give sufficient geometric conditions to ensure the uniform boundedness of periodic solutions, obtain an upper bound of the period of nonconstant periodic solutions in a connected compo...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Periodic solutions of a singularly perturbed delay differential equation

A singularly perturbed differential delay equation of the form ẋ(t) = −x(t)+ f (x(t − 1), λ) (1) exhibits slowly oscillating periodic solutions (SOPS) near the first period-doubling bifurcation point of the underlying map (obtained by setting = 0). For extremely small values of , these periodic solutions resemble square waves, which consist of sharp, O( ) transition layers connecting intervals ...

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...