Monotonous stability for neutral fixed points

Monotonous stability for neutral fixed points

We give subtle, simple and precise results about the convergence or the divergence of the sequence (xn), where xj = f(xj−1) for every integer j, when the initial element x0 is in the neighbourhood of a neutral fixed point, i.e. a point x∗ such that f(x∗) = x∗ with |f ′(x∗)| = 1 (where f is a C∞ function defined on a subset of R).

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...

Fixed Points, Stability, and Harmless Perturbations

Much has been written about systems in which each constant is a solution and each solution approaches a constant. It is a small step to conjecture that functions promoting such behavior constitute harmless perturbations of stable equations. That idea leads to a new way of avoiding delay terms in a functional-differential equation. In this paper we use fixed point theory to show that such a conj...