Oscillation Criteria for Matrix Differential Equations

Abstract

We shall be concerned at first with some properties of the solutions of the matrix differential equation 1.1 where is an n × n symmetric matrix whose elements are continuous real-valued functions for 0 < x < ∞, and Y(x) = (y_ij(x)), Y″(x) = (y″ _ij(x)) are n × n matrices. It is clear such equations possess solutions for 0 < x < ∞, since one can reduce them to a first-order system and then apply known existence theorems (6, Chapter 1).