Oscillatory Properties of Certain Nonlinear Matrix Differential Systems of Second Order

where Y, Z, Kix) and G(x) are « x n matrices and each of Kix) and G(x) is a symmetric matrix of continuous functions on a z% x < oo. By a solution of (b) we mean a pair of n x n matrices {T(x),Z(x)} such that each of the elements of Y and Z is a differentiable function and such that {Y,Z} satisfies the initial condition and satisfies the matrix differential system almost everywhere on a S! x < oo. The roles of the sine and cosine functions in the polar coordinate transformation are assumed by the solution pair of « x n matrices [S[a,x; Q], C[a,x; g]} of the linear matrix differential system