Regularity and nonoscillation of solutions to second-order linear differential equations.(English)Zbl 0947.34015

It is proved that oscillation / nonoscillation criteria of the Kneser-Hille type imply also regularity in the sense of Karamata of all nonoscillatory solutions to the equation $y^{{\prime}{\prime}}+f(x)y=0,$ where f(x) is continuous and of arbitrary sign on some positive halfaxis.

MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 26A12 Rate of growth of functions, orders of infinity, slowly varying functions