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Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
In this work we investigate the dynamics of the nonlinear DDE (delay-differential equation) x''(t)+x(t-T)+x(t)^3=0 where T is the delay. For T=0 this system is conservative and exhibits no limit cycles. For T>0, no matter how small, an…
We unify two different periodicity mechanisms: delayed self-regulation and planar predator-prey feedback. We consider scalar delay differential equations $\dot x(t) = rf(x(t), x(t - 1))$ where $f$ is monotone in the delayed component. Due…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…
The delayed Duffing equation $\ddot{x}(t)+x(t-T)+x^3(t)=0$ is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that $T^2<\tfrac{3}{2}\pi^2$. In…
We consider a parabolic PDE with Dirichlet boundary condition and monotone operator $A$ with non-standard growth controlled by an $N$-function depending on time and spatial variable. We do not assume continuity in time for the $N$-function.…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…
We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
We consider differential delay equations of the form $\partial_tx(t) = X_{t}(x(t - \tau))$ in $\mathbb{R}^n$, where $(X_t)_{t\in S^1}$ is a time-dependent family of smooth vector fields on $\mathbb{R}^n$ and $\tau$ is a delay parameter. If…
The aim of this paper is to provide an effective framework for analysing bifurcations of equilibria in nonlinearly periodically forced delay differential equations. First, we establish the existence of a periodic smooth finite-dimensional…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…