A note on asymptotic integration of second order nonlinear differential equations

Abstract

The paper is concerned with the asymptotic behavior of solutions to a second order nonlinear differential equation u + f(t, u) = 0. Using the Banach contraction principle, we establish global existence of solutions which satisfy u(t) = At + o(t(nu)) as t --> +infinity, where A is an element of R and nu is an element of (0, 1].