@article {
author = {Yankson, Ernest},
title = {Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays},
journal = {Khayyam Journal of Mathematics},
volume = {3},
number = {1},
pages = {1-11},
year = {2017},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2017.43831},
abstract = {Necessary and sufficient conditions for the zero solution of the nonlinear neutral integro-differential equation\begin{eqnarray*}&&\frac{d}{dt}\Big(r(t)\Big[x(t)+Q(t, x(t-g_1(t)),...,x(t-g_N(t)))\Big]\Big)\\ &&= -a(t)x(t)+ \sum^{N}_{i=1}\int^{t}_{t-g_i(t)}k_i(t,s)f_i(x(s))ds \end{eqnarray*} to be asymptotically stable are obtained. In the process we invert the integro-differential equation and obtain an equivalent integral equation. The contraction mapping principle is used as the main mathematical tool for establishing the necessary and sufficient conditions.},
keywords = {Stability,integro-differential equation,functional delay},
url = {http://www.kjm-math.org/article_43831.html},
eprint = {http://www.kjm-math.org/article_43831_2161050be631ca19a702fe6a0bd6d1c3.pdf}
}