Method for Studying the Asymptotic Properties of Solutions to a System of Second-Order Linear Differential Equations on the Half-Line

Abstract

A special method is proposed for reducing an $$n $$-dimensional system of second-order ordinary differential equations to a $$2n$$-dimensional system of first-order ones. Using matrix weight functions (which can be chosen arbitrarily when applying the method), we establish sufficient conditions for the boundedness and power-law absolute integrability on the half-line of the components of all solutions to a linear system of second-order differential equations and their first derivatives as well as for their decay (in particular, exponential or power-law) as the independent variable tends to infinity. An illustrative example is provided.