Transformation der Lösungen der Systeme von vier linearen Differentialgleichungen 1. Ordnung
A survey of investigations of linear differential equations from the point of view of transformations is described. These investigations started in the middle of the last century and continued till the present time. Essential step was done in the fifties by O. Borvka, who started global investigations of the second order equations.
The existence of bounded solutions for equations in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation satisfies some conditions expressed in terms of measures of noncompactness.