Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A new nonlinear impulsive delay differential inequality and its applications | Wang and Ding Journal of Inequalities and Applications 2011 2011 11 http content 2011 1 11 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access A new nonlinear impulsive delay differential inequality and its applications Huali Wang and Changming Ding Correspondence cding@. School of Mathematical Sciences Xiamen University Xiamen 361005 PR China SpringerOpen0 Abstract In this article a new nonlinear impulsive delay differential inequality is established which can be applied in the dynamical analysis of nonlinear systems to improve many extant results. Using the inequality we obtain some sufficient conditions to guarantee the exponential stability of nonlinear impulsive functional differential equations. Two examples are given to illustrate the effectiveness and advantages of our results. Keywords Impulsive delay differential inequality exponential stability nonlinear functional differential systems 1. Introduction It is well known that the theory of differential inequalities plays an important role in the qualitative and quantitative studies of differential equations 1-3 . In recent years various inequalities have been established such as the Halanay inequalities in 4-6 the delay inequalities in 7-10 and the impulsive differential inequalities in 11-13 . Using the linear inequality techniques many results have been done on the stability and dynamical behavior for differential systems see 4-13 and the references cited therein. For example 11 presents an extended impulsive delay Halanay inequality and deals with the global exponential stability of impulsive Hopfield neural networks with time delays. In 13 the authors establish a delay differential inequality with impulsive initial conditions and derive some sufficient conditions ensuring the exponential stability of solutions for the impulsive differential equations. However linear differential inequalities do not work in the .
