相关论文: Delay Equations of the Wheeler-Feynman Type
We study the equations of Wheeler-Feynman electrodynamics which is an action-at-a-distance theory about world-lines of charges that interact through their corresponding advanced and retarded Li\'enard-Wiechert field terms. The equations are…
We rigorously construct a variety of orbits for certain delay differential equations, including the electrodynamic equations formulated by Wheeler and Feynman in 1949. These equations involve delays and advances that depend on the…
The equations for the electromagnetic two-body problem are neutral-delay equations that for generic initial data have solutions with discontinuous derivatives. If one wants to use these neutral-delay equations with arbitrary initial data,…
We generalize Wheeler-Feynman electrodynamics with a variational boundary-value problem with past and future boundary segments that can include velocity discontinuity points. Critical-point trajectories must satisfy the Euler-Lagrange…
In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant…
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…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
The problem of 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with retarded and advanced interactions is investigated.
In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carath\'eodory type right-hand side functions. We provide construction of randomized Euler scheme for DDEs and…
We consider delay differential equations of the form $ y'(t)=-ay(t)+bf(y(t-1)) $ with positive parameters $a,b$ and a unimodal $f:[0,\infty)\to [0,1]$. It is assumed that the nonlinear $f$ is close to a function $g:[0,\infty)\to [0,1]$ with…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
The direct interaction theory of electromagnetism, also known as Wheeler-Feynman electrodynamics, is often misinterpreted and found unappealing because of its reference to the absorber and, more importantly, to the so-called absorber…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
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…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…