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

摘要

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) is considered, and Lyapunov's 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.