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

Howard, H. C.; Marić, V.

Bull., Cl. Sci. Math. Nat., Sci. Math. 114, No. 22, 85-98 (1997).

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.

Reviewer: Julka Miljanović-Knežević (Zemun)

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

Keywords:

second-order linear equations; regular variation; Karamata class