Asymptotic quiescent position for systems of homogeneous non-autonomous differential equations

A system of homogeneous non-autonomous differential equations with disturbed right-hand parts is considered. The zero solution doesn’t exist for the considered system but the question about behavior of solutions starting near zero is still open. Conditions for existing of asymptotic quiescent position are determined if the right parts of the system satisfies provided conditions. A corresponding theorem is proved based on second Lyapunov method which allows to use the provided function for further researches. In conclusion an illustrative example is given which avows obtained results. Bibliogr. 5. Il. 1.