%0 Journal Article
%T Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Yankson, Ernest
%D 2017
%\ 01/01/2017
%V 3
%N 1
%P 1-11
%! Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays
%K Stability
%K integro-differential equation
%K functional delay
%R 10.22034/kjm.2017.43831
%X Necessary and sufficient conditions for the zero solution of the nonlinear neutral integro-differential equationbegin{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.
%U http://www.kjm-math.org/article_43831_2161050be631ca19a702fe6a0bd6d1c3.pdf