On the asymptotic behavior of solutions of certain second-order differential equations

In this paper, the second order non-linear differential equation x ¨ + a ( t ) f ( x , x ˙ ) x ˙ + b ( t ) g ( x ) = p ( t , x , x ˙ ) sidered, and Lyapunovʹs second method is used to show that uniform boundedness and convergence to zero of all solutions of this equation together with their derivatives of the first order.