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

Estimates of Periods and Global Continua of Periodic Solutions for State-Dependent Delay Equations

We study the global Hopf bifurcation of periodic solutions for one-parameter systems of state-dependent delay differential equations, and specifically we obtain a priori estimates of the periods in terms of certain values of the state-dependent delay along continua of periodic solutions in the Fuller space C(R;RN+1) × R2. We present an example of three-dimensional state-dependent delay differen...

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

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Slowly Oscillating Periodic Solutions of Autonomous State-dependent Delay Equations

IT HAS BEEN more than a dozen years since the peak of activity on the question of the existence of periodic, slowly oscillating, solutions of autonomous delay differential equations. Following the early work of Jones [l], Wright [2] and Grafton [3], the work of Nussbaum [4, 51 is to be specially noted for providing several new fixed point results and a global bifurcation theorem which are parti...

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

Boundary layer phenomena for differential-delay equations with state-dependent time lags: III

We consider a class of singularly perturbed delay-differential equations of the form e ’ xðtÞ 1⁄4 f ðxðtÞ; xðt rÞÞ; where r 1⁄4 rðxðtÞÞ is a state-dependent delay. We study the asymptotic shape, as e-0; of slowly oscillating periodic solutions. In particular, we show that the limiting shape of such solutions can be explicitly described by the solution of a pair of so-called max-plus equations. ...