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.
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
MLA
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
HARVARD
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
VANCOUVER
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