-asymptotic stability by fixed point in neutral nonlinear differential equations with delay

On Positive Solutions of a Fourth Order Nonlinear Neutral Delay Difference Equation

“…Let the mappings and : Ω 1 ( , ) → ∞ be defined by (15) and (16), respectively. By means of (12), (15), (16), (32), and (33), we infer that for any = { } ∈Z , = { } ∈Z ∈ Ω 1 ( , ), and ≥ ,…”

“…By employing a few famous tools in nonlinear analysis including the nonlinear alternative of Leray-Schauder type, Banach's fixed point theorem, Schauder's fixed point theorem, Krasnoselskii's fixed point theorem, coincidence degree theory and critical point theory, the authors [3, 4, 9, 13-16, 18, 25, 27, 28] and others proved the existence of nonoscillatory solutions, uncountably many bounded nonoscillatory solutions and periodic solutions for the difference equations above, where Lipschitz conditions were used in [14,16]. Recently, the authors [32] used the Krasnoselskii's fixed point theorem to obtain ℎ-asymptotic stability results about the zero solution for a very general first order nonlinear neutral differential equation with functional delay.…”

Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument

“…Thus the existence of fixed points for the sum of two operators has attracted tremendous interest, and their applications are frequent in nonlinear analysis. See [ 32 , 33 , 43 – 46 ].…”

New criteria for stability of neutral differential equations with variable delays by fixed points method

“…Zhou and Zhong [15] study the exponential p-stability of neutral stochastic differential equations with multiple delays. Pinto and Seplveda [16] talk about H-asymptotic stability by the fixed point method in neutral nonlinear differential equations with delay. By the same method, Equation 1 and its generalization have been investigated by many authors.…”