Related papers: On Nonoscillation of Mixed Advanced-Delay Differen…
We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms $$ \dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))- \sum_{k=1}^l b_k(t)x(g_k(t))=0 $$ and its modifications, and apply…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
In this paper, we investigate the well-posedness and asymptotic behavior of difference equations of the form $x(t) = A x(t - \tau(t))$, $t \geq 0$, where the unknown function $x$ takes values in $\mathbb R^d$ for some positive integer $d$,…
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…
Simple form scalar differential equation with delay and non-linear negative periodic feedback is considered. The existence of slowly oscillating periodic solutions with the same period as the feedback coefficient is shown numerically within…
Conditions are given for a class of nonlinear ordinary differential equations x''(t)+a(t)w(x)=0, t>=1, which includes the linear equation to possess solutions x(t) with prescribed oblique asymptote that have an oscillatory pseudo-wronskian…
A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
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 goal of our work is to investigate the oscillation and asymptotic properties of a class of difference equations with a condition. In contrast to most previous studies, the oscillation of the investigated equation is obtained with only…
Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…
We investigate the time-asymptotic properties of solutions of the differential equation x''(t) + a(t)x'(t) + g(x(t)) = 0 in a Hilbert space, where a(.) is non-increasing and g is the gradient of a potential G. If the coefficient a(.) is…
In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…
We propose here a delay differential equation that exhibits a new type of resonating oscillatory dynamics. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. The…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^{\alpha} x(t) = g\left(x(t-\tau_1), x(t-\tau_2)\right)$ involving two delays viz. $\tau_1\geq…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
In this paper, we give explicit exponential estimates $\displaystyle |x(t)|\leq M e^{ -\gamma (t-t_0) }$, where $t\geq t_0$, $M>0$, for solutions of a linear scalar delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m…