Yankson, E. (2017). Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays. Khayyam Journal of Mathematics, 3(1), 1-11. doi: 10.22034/kjm.2017.43831

Ernest Yankson. "Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays". Khayyam Journal of Mathematics, 3, 1, 2017, 1-11. doi: 10.22034/kjm.2017.43831

Yankson, E. (2017). 'Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays', Khayyam Journal of Mathematics, 3(1), pp. 1-11. doi: 10.22034/kjm.2017.43831

Yankson, E. Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays. Khayyam Journal of Mathematics, 2017; 3(1): 1-11. doi: 10.22034/kjm.2017.43831

Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays

^{}Department of Mathematics and Statistics, University of Cape Coast, Cape Coast, Ghana.

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.