Stability, boundedness and unique global solutions to certain second order nonlinear stochastic delay differential equations with multiple deviating arguments

Abstract

In this paper, asymptotic stability, boundedness and uniqueness of global solution to certain second order stochastic delay differential equations with multiple deviating arguments is considered. By using the second method of Lyapunov, a perfect Lyapunov functional is constructed and used to obtain suitable conditions on the nonlinear functions to guarantee uniqueness of solution, asymptotic stability and boundedness of solutions. The obtained results are new, extend and form a complement to some known recent results in the literature. Moreover, examples are given to show the genuineness and originality of the obtained results.