Stability by Krasnoselskii’s theorem in totally nonlinear neutral differential equations

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

Neutral stochastic functional differential equations NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper i...

Stability by Krasnoselskii Fixed Point Theorem for Neutral Nonlinear Differential Equations with Variable Delays Abdelouaheb Ardjouni and Ahcene Djoudi

We use Krasnoselskii’s fixed point theorem to obtain boundedness and stability results about the zero solution of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the works of C. H. Jin and J. W. Luo [12] and also those of [5, 9, 15]. In the end we provide an examp...

Stability by Contraction Mapping in Nonlinear Neutral Differential Equations with Variable Delay

The nonlinear neutral differential equation x′ (t) = −a (t) g (x (t− τ (t))) + c (t)x′ (t− τ (t)) , with variable delay τ (t) ≥ 0 is investigated. We find suitable conditions for τ , a, c and g so that for a given continuous initial function ψ a mapping P for the above equation can be defined on a carefully chosen complete metric space S0 ψ in which P possesses a unique fixed point. The final r...

Stability analysis of nonlinear hybrid delayed systems described by impulsive fuzzy differential equations

In this paper we introduce some stability criteria of nonlinear hybrid systems with time delay described by impulsive hybrid fuzzy system of differential equations. Firstly, a comparison principle for fuzzy differential system based on a notion of upper quasi-monotone nondecreasing is presented. Here, for stability analysis of fuzzy dynamical systems, vector Lyapunov-like functions are defined....