Über das asymptotische Verhalten der Lösungen einer linearen Differentialgleichung mit Nachwirkung

Abstract

In the paper for the differential equation

necessary conditions and sufficient conditions for the existence of eventually positive solutions are given which generalize known conditions. Their eventually positive solutions are estimated by means of solutions of the related differential inequalities. Finally an expansion theorem is proved. The results are mainly based on the consideration of the solutions of the differential inequalities and the application of comparison theorems for these solutions.