Nonoscillation and disconjugacy of systems of linear differential equations

AbstractThe differential equations under consideration are of the form dxdt = A(t)x, (1) where A(t) is a piecewise continuous real n × n matrix on a real interval α, and the vector x = (x1,…,xn) is continuous on α. The equation is said to be nonoscillatory on α if every nontrivial real solution vector x has at least one component xk which does not vanish on α.The principal concern of this paper is the derivation of conditions, expressed in terms of various norms of A, which guarantee the nonoscillation of (1) in a given interval