Investigation of convergence of large scale almost periodic systems by means of comparison vector functions with components as forms of even degrees

Abstract

By V. M. Matrosov’s comparison method we obtain sufficient conditions of convergence for a large scale almost periodic system of differential equations. As components of comparison vector functions we use the homogeneous forms of even degrees. We propose a new approach to construction of comparison system that leads to the best resultswith respect to known F.N. Bailey’s, D. D. Siljak’s and V. D. Furasov’s approaches.