Fixed points and stability in differential equations with variable delays

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...

Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays

Fixed Points and Stability in Neutral Nonlinear Differential Equations with Variable Delays

Abstract. By means of Krasnoselskii’s fixed point theorem we obtain boundedness and stability results 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 work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307–3315], and also those of T.A. Burton [Fixed ...

Fixed Points and Stability in Nonlinear Neutral Volterra Integro-differential Equations with Variable Delays

Abstract. In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a necessary and sufficient condi...

Stability in Nonlinear Neutral Differential Equations with Variable Delays Using Fixed Point Theory

Abstract. The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient functions to change sign and do not require bounded delays. The obtained results improve an...