Asymptotic integration of linear differential equations (Q1363592)

The authors establish a new result on the asymptotic integration of linear differential equations of the form \(y'=(\Lambda+R)y\), where \(\Lambda\) is diagonal and \(R\) ist small. The result lies between the basic theorems of Levinson and of Hartman-Wintner [see, for example, \textit{M. S. P. Eastham} and \textit{C. G. M. Grudniewicz}, J. Lond. Math. Soc., II. Ser. 24, 255-271 (1981; Zbl 0477.34040)] and also treats quite different situations. One main assumption is a refined dichotomy condition on the real parts of the elements of the diagonal Matrix \(\Lambda\). As the authors show in an example this allows less restrictive assumptions for results usefull when calculating deficiency indices of differential expressions or doing spectral analysis of differential operators.