Asymptotic Integration of Perturbed Linear Differential Equations under Conditions Involving Ordinary Integral Convergence

In this paper, we consider asymptotic integration of nth order linear differential equations with constant coefficients, modified by the addition of small functions. The integral smallness of the perturbation functions is expressed in terms of ordinary convergence instead of the classic conditions which require absolute integrability. The proof of our result is based on the Banach contraction principle.