Generalized Mean Square Exponential Stability for Stochastic Functional Differential Equations
MathematicsThis work focuses on a class of stochastic functional differential equations and neutral stochastic differential functional equations. By using a new approach, some sufficient conditions are obtained to guarantee the generalized mean square exponential ...
Tianyu He, Zhi Li, Tianquan Feng
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Explicit stability conditions for neutral type vector functional differential equations. A survey [PDF]
Surveys in Mathematics and its Applications, 2014 This paper is a survey of the recent results of the author on the stability of linear and nonlinear neutral type functional differential equations. Mainly, vector equations are considered. In particular, equations whose nonlinearities are causal mappings
Michael I. Gil'
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Adams methods for neutral functional differential equations
Numerische Mathematik, 1982 In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a "non-smooth" solution the order of convergence is only one ...
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Existence of positive periodic solutions for neutral functional differential equations
Electronic Journal of Differential Equations, 2006 We find sufficient conditions for the existence of positive periodic solutions of two kinds of neutral differential equations. Using Krasnoselskii's fixed-point theorem in cones, we obtain results that extend and improve previous results.
Zhixiang Li, Xiao Wang
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Periodic solutions for neutral nonlinear differential equations with functional delay
Electronic Journal of Differential Equations, 2003 We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with functional delay $$ x'(t) = -a(t)x(t)+ c(t)x'(t-g(t))+ q(t, x(t), x(t-g(t)) $$ has a periodic solution.
Youssef N. Raffoul
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Critical cases for neutral functional differential equations
Journal of Differential Equations, 1971 Neutral functional equation including scalar differential-difference equation, determining sufficient conditions for zero ...
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Oscillation of solutions to odd-order nonlinear neutral functional differential equations
Electronic Journal of Differential Equations, 2011 In this note, we establish some new comparison theorems and Philos-type criteria for oscillation of solutions to the odd-order nonlinear neutral functional differential equation $$ [x(t)+p(t)x(au(t))]^{(n)}+q(t)x^alpha(sigma(t))=0, $$ where $0leq p(
Tongxing Li, Ethiraju Thandapani
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Uniform exponential stability of linear periodic systems in a Banach space
Electronic Journal of Differential Equations, 2001 This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic ...
David N. Cheban
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Uniform exponential stability of linear almost periodic systems in Banach spaces
Electronic Journal of Differential Equations, 2000 This article is devoted to the study linear non-autonomous dynamical systems possessing the property of uniform exponential stability. We prove that if the Cauchy operator of these systems possesses a certain compactness property, then the uniform ...
David N. Cheban
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A Massera type criterion for a partial neutral functional differential equation
Electronic Journal of Differential Equations, 2002 We prove the existence of periodic solutions for partial neutral functional differential equations with delay, using a Massera type criterion.
Eduardo Hernandez M.
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