Mathematics, 2022 This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler ...
Qi Wang, Huabin Chen, Chenggui Yuan
doaj +1 more source
On Neutral Functional–Differential Equations with Proportional Delays
Journal of Mathematical Analysis and Applications, 1997 The paper deals with the well-posedness of the initial value problem for the neutral functional-differential equation \[ y'(t)= ay(t)+ \sum_{i=1}^\infty b_iy(q_it)+ \sum_{i=1}^\infty cy'(p_it), \qquad t>0, \quad y(0)=y_0 \] and the asymptotic behaviour of its solutions.
Iserles, Arieh, Liu, Yunkang
openaire +2 more sources
Oscillatory behaviour of a higher order nonlinear neutral delay type functional differential equation with oscillating coefficients [PDF]
, 2005 summary:In this paper we are concerned with the oscillation of solutions of a certain more general higher order nonlinear neutral type functional differential equation with oscillating coefficients.
Akin, Ömer, Bolat, Yaşar
core +1 more source
Global existence results for second order neutral functional differential equation with state-dependent delay [PDF]
, 2016 summary:Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay.
Medjadj, Imene, Benchohra, Mouffak
core +1 more source
Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay [PDF]
Opuscula Mathematica, 2012 We use a variant of Krasnoselskii's fixed point theorem by T. A. Burton to show that the nonlinear neutral differential equation with functional delay \[x'(t) = -a(t)h(x(t)) +c(t)x'(t-g(t)) + q(t,x(t) x(t-g(t)))\] has a periodic solution.
Ernest Yankson
doaj +1 more source
Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator [PDF]
, 2022 summary:In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation \[ \big (y(t)- \sum _{i=1}^k p_i(t) y(r_i(t))\big )^{(n)}+ v(t)G( y(g(t)))-u(t)H(y(h(t))) = f(t) \] oscillates or tends to zero as $t ...
Rath, R.N., Rath, S.K., Panda, K.C.
core +1 more source
Asymptotic stability of a neutral integro-differential equation [PDF]
Opuscula Mathematica, 2006 The global stability behavior of a non-autonomous neutral functional integro-differential equation is studied. A sufficient condition for every solution of this equation to tend to zero is given.
Gen-qiang Wang, Sui Sun Cheng
doaj
A class of Neutral Functional Differential Equations
Journal of Differential Equations, 1972 Formulation and study of the initial value problem for neutral functional differential equations. The existence, uniqueness, and continuation of solutions to this problem are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem ...
openaire +2 more sources
A Neutral Functional Differential Equation with an Unbounded Kernel
Journal of Integral Equations and Applications, 1993 The authors consider the scalar neutral functional differential equation (1) \((d/dt) \int^ 0_{-\infty} g(s)u(t + s)ds = 0\) for \(t \in [0,\infty)\), \(u(t) =\varphi (t)\) for \(t0\), with norm \(\| f \|^ 2 = \int^ 0_{-\infty} e^{-\omega s} h(s)f^ 2(s)ds\).
Turi, Janos, Desch, Wolfgang
openaire +3 more sources
Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching [PDF]
, 2008 The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching.
Yuan, Chenggui +4 more
core +4 more sources