Related papers: Delayed Gronwall inequality with weakly singular k…
This paper considers linear delay-difference equations, that is, equations relating the state at a given time with its past values over a given bounded interval. After providing a well-posedness result and recalling Hale--Silkowski…
The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent…
Starting from the coordinate system used by Einstein to find the bending of light rays by gravitational fields we calculate the effect of the Earth gravitational energy along a hypothetical photon null path on the geoid non inertial system.…
We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an…
The paper provides two versions of nonlocal Poincar\'e-type inequalities for integral operators with a convolution-type structure and functions satisfying a zero-Dirichlet like condition. The inequalities extend existing results to a large…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities together with a continuity argument, we…
The sufficient conditions for existence and uniqueness of continuous solutions of the Volterra operator equations of the first kind with piecewise continuous kernel are derived. The asymptotic approximation of the parametric family of…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the…
We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…
This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…
It is shown that the transmission and reflection group delay times in an asymmetric single quantum barrier are greatly enhanced by the transmission resonance when the energy of incident particles is larger than the height of the barrier.…
A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…
This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those…
The following class of retarded integro-differential equations in a Banach space \[ \dot{x}\left(t\right)=Ax\left(t\right)+\int_{0}^{t}b\left(t-\tau\right)Lx_{\tau}d\tau+Kx_{t};\,\,t\geq0, \] are taken into consideration in this study. The…
In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
The late-time behavior of a scalar field on fixed Kerr background is examined in a numerical framework incorporating the techniques of conformal compactification and hyperbolic initial value formulation. The applied code is 1+(1+2) as it is…
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent…