Oscillation of Nonlinear Systems of Matrix Differential Equations
Athanassios G. Kartsatos · Proceedings of the American Mathematical Society · 1971
For systems of matrix equations of the form \[ U’ = A(t,U,V)V,\quad V’ = - B(t,U,V)\] it is shown here that the oscillation problem can be reduced to the corresponding problem of “associated” (in some sense) scalar equations for which there exist numerous results. Furthermore, it is also shown that many of the existing results concerning the equation \[ (A(t)U’)’ + B(t,U,U’)U = 0\] can be considerably improved by application of the above method.