Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :New criteria for stability of neutral differential equations with variable delays by fixed points method | Zhao Advances in Difference Equations 2011 2011 48 http content 2011 1 48 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access New criteria for stability of neutral differential equations with variable delays by fixed points method Dianli Zhao1 2 Correspondence Tc_zhaodianli@ 1College of Science University of Shanghai for Science and Technology Shanghai 200093 China Full list of author information is available at the end of the article Springer Abstract The linear neutral differential equation with variable delays is considered in this article. New criteria for asymptotic stability of the zero solution are established using the fixed point method and the differential inequality techniques. By employing an auxiliary function on the contraction condition the results of this article extend and improve previously known results. The method used in this article can also be used for studying the decay rates of the solutions. Keywords fixed points stability neutral differential equation variable delays 1 Introduction The objective of this article is to investigate the stability of the zero solution of the first-order linear neutral differential equations with variable delays x t -b t x t - T t c t x t - T t 1 and it s generalized form N M x t -a t x t - bj t g x t - Tj t Cj t x t - Tj t 2 by fixed point method under assumptions a b c bj Cj e C R R T Tj e C R R t - T t and t - Tj t as t . Recently Burton and others 1-10 applied fixed point theory to study stability. It has been shown that many of problems encountered in the study of stability by means of the Lyapunov s direct method can be solved by means of the fixed point theory. Then together with Sakthivel and Luo 11 12 investigate the asymptotic stability of the nonlinear impulsive stochastic differential equations and the impulsive stochastic partial differential equations with infinite delays by means of the fixed point theory. On the other hand .
