Oscillation of nonlinear matrix differential equations of second order.
E. C. Tomastik · Proceedings of the American Mathematical Society · 1968
where U= (uij), F= (fij) and R are nXn matrices. By F= F(t, U, U') is meant fij=fj;(t, ul, , unn, u, * , u). The functions fij are assumed to be continuous for t on [a, so ), a > 0, and for all values of the remaining variables. The matrix F(t, U, U') is symmetric and positive definite for every t on [a, co) and every matrix U with det U O, while the matrix R(t) is continuous, symmetric and positive definite for every t on [a, oo ). Equation (1) is equivalent to a system of n2 second order equations or to 2n2 first order differential equations and so any existence and uniqueness theorem for such systems will apply to (1). We merely assume here that we do have existence and uniqueness for the system tive (1) together with the boundary condition