Stability in nonlinear neutral integro-differential equations with variable delay using fixed point theory

被引：4
作者：
Ardjouni A. [1 ]
Djoudi A. [1 ]
机构：
[1] Faculty of Sciences, Department of Mathematics, Badji Mokhtar, University of Annaba, Annaba 23000
来源：
Journal of Applied Mathematics and Computing | 2014年 / 44卷 / 1-2期
关键词：
Fixed points; Integro-differential equation; Stability; Variable delays;
D O I：
10.1007/s12190-013-0695-8
中图分类号：
学科分类号：
摘要：
The nonlinear neutral integro-differential equation d/dt x(t) = - ∫t-τ(t)t a(t, s)g(x(s))ds + d/dtG(t, x(t - τ(t)), with variable delay τ(t)≥0 is investigated. We find suitable conditions for τ, a, g and G so that for a given continuous initial function ψ a mapping P for the above equation can be defined on a carefully chosen complete metric space Sψ0 in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient condition. The obtained theorem improves and generalizes previous results due to Burton (Proc. Am. Math. Soc. 132:3679-3687, 2004), Becker and Burton (Proc. R. Soc. Edinb., A 136:245-275, 2006) and Jin and Luo (Comput. Math. Appl. 57:1080-1088, 2009). © 2013 Korean Society for Computational and Applied Mathematics.
引用
收藏
页码：317 / 336
页数：19
相关论文
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