Integral criteria for a classification of solutions of linear differential equations

are positive continuous function on the interval [0, + co). By solution we always mean a continuously differentiable function such that r(t) x’(t) has a continuous derivative satisfying (E,). When the func- tion r is continuous but does not have a continuous derivative, (E,) can be interpreted as the first order system for the vector (x, y) = (x, rx’). 381