On the Stability and Boundedness of Solutions of Certain Kind of Second Order Delay Differential Equations

On the Stability and Boundedness

Abstract

In this paper, we study the second order non-autonomous nonlinear delay differential equation
$$x^{\prime\prime} + b(t)g(x,x^\prime) + c(t)h(x(t-r))m(x^\prime) = p(t,x,x^\prime)$$
for asymptotic stability of solutions when $p(t,x,x^\prime) = 0$ and the boundedness of solutions when $p(t,x,x^\prime) \neq 0.$ This work improved on some earlier results in the literature.