Nonlinear functionals and a theorem of Sun

We use a recently developed theory of nonlinear functionals in the study of oscillations of second-order symmetric vector differential systems to extend a number of theorems of Sun [New Kamenev type theorems for second order linear matrix differential systems, Appl. Math. Lett., 2004, in press] under a common theme. The criteria presented here are of the form: the integral of the coefficient matrix is bounded at infinity (in a sense to be made explicit in the paper) and bounded away from a positive absolute constant implies oscillation at infinity.