TY - JOUR
A2 - Han, Zhen-Lai
AU - Abou-El-Ela, A. M. A.
AU - Sadek, A. I.
AU - Mahmoud, A. M.
AU - Taie, R. O. A.
PY - 2015
DA - 2015/03/31
TI - On the Stochastic Stability and Boundedness of Solutions for Stochastic Delay Differential Equation of the Second Order
SP - 358936
VL - 2015
AB - We present two qualitative results concerning the solutions of the following equation: x¨(t)+g(x˙(t))+bx(t-h)+σx(t)ω˙(t)=p(t,x(t),x˙(t),x(t-h)); the first result covers the stochastic asymptotic stability of the zero solution for the above equation in case p≡0, while the second one discusses the uniform stochastic boundedness of all solutions in case p≢0. Sufficient conditions for the stability and boundedness of solutions for the considered equation are obtained by constructing a Lyapunov functional. Two examples are also discussed to illustrate the efficiency of the obtained results.
SN - null
UR - https://doi.org/10.1155/2015/358936
DO - 10.1155/2015/358936
JF - Chinese Journal of Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -