On the existence of solutions with prescribed asymptotic behaviour for perturbed nonlinear differential equations of second order
A global existence result for solutions u(t) of the differential equation x" + f(t, x) = p(t), t >= t(0) >= 1, that can be written as u(t) = P(t) + o(l) for all large t, where P"(t) = p(t), is established by means of the Schauder-Tikhonov theorem. It generalizes the recent work of Lipovan [On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Gla