TY - JOUR
ID - 43831
TI - Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Yankson, Ernest
AD - Department of Mathematics and Statistics, University of Cape Coast, Cape
Coast, Ghana.
Y1 - 2017
PY - 2017
VL - 3
IS - 1
SP - 1
EP - 11
KW - Stability
KW - integro-differential equation
KW - functional delay
DO - 10.22034/kjm.2017.43831
N2 - 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.
UR - http://www.kjm-math.org/article_43831.html
L1 - http://www.kjm-math.org/article_43831_2161050be631ca19a702fe6a0bd6d1c3.pdf
ER -