The Condition of Ordinary Integral Convergence in the Asymptotic Theory of Linear Differential Equations With Almost Constant Coefficients

In this paper, we continue the work started in [2], wherethe asymptotic integration of nth order linear differential equations was considered under smallness conditions, expressed in terms of ordinary integral convergence. The method of integration in [2] was based on using the Banach contraction principle for a linear nonhomogeneous operator in a Banach space. In this paper, we use the same principle for a nonlinear operator which corresponds to the equation for the logarithmic derivative of the original dependent variable. The result proved concerns a class of equations considered in [2] under essential additional restrictions.