相关论文: Boundedness and Stability of Impulsively Perturbed…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty $. Suppose each solution of the corresponding…
The paper is concerned with stabilization of a scalar delay differention equation $$ {\dot x}(t) - \sum_{k=1}^m A_k(t)x[h_k(t)] = 0,~t\geq 0,~ x(\xi)=\varphi (\xi), \xi <0, $$ by introducing impulses in certain moments of time $$ x(\tau_j)…
The connection of function properties of solutions with exponential stability of linear impulsive differential equation $$\dot{x} (t) - \sum_{k=1}^m {A_k (t) x[h_k(t)]} = r(t),~ t \geq 0, x(\xi ) = \varphi (\xi),~ \xi < 0,$$ $$x(\tau_j) =…
For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…
New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m a_k(t)x(h_k(t))=0 $$ with measurable delays and coefficients. These…
The main result of the paper is that the oscillation (non-oscillation) of the impulsive delay differential equation $\dot {x}(t)+\sum_{k=1}^m A_k(t)x[h_k(t)]=0,~~t\geq 0$, $x(\tau_j)=B_jx(\tau_j-0), \lim \tau_j = \infty$ is equivalent to…
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…
New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation $$ \dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))+\int_{g(t)}^t K(t,s) x(s)ds=0, $$ where $h_k(t)\leq t$, $g(t)\leq…
An extensive overview of existing criteria, as well as some new uniform exponential stability tests are included for a scalar delay equation $$ \dot{x}(t)+ \sum_{j=1}^n a_j(t)x(h_j(t))=0. $$ Both cases of continuous and measurable…
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…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays $$ (x(t)-a(t)x(g(t)))'=-b(t)x(h(t)), $$ where $|a(t)|<1$, $b(t)\geq 0$, $h(t)\leq t$, $g(t)\leq t$, in…
For the delay differential equations $$ \ddot{x}(t) +a(t)\dot{x}(g(t))+b(t)x(h(t))=0, g(t)\leq t, h(t)\leq t, $$ and $$ \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)+a_1(t)\dot{x}(g(t))+b_1(t)x(h(t))=0 $$ explicit exponential stability conditions…
We study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear…
We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $$ \dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0, $$ where $$ |a(t)|<1,~ b(t)\geq 0,…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
\noindent Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \begin{equation*} \Delta \left(r_{n}\left(\Delta \left(x_{n}+p_{n}x_{n-k}\right) \right)…