Nonoscillatory half-linear differential equations and generalized Karamata functions

We introduce a natural generalization of the concept of regularly varying functions in the sense of Karamata, and show that the class of generalized Karamata functions is a well-suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half-linear differential equation of the type (A) ( p ( t ) | y ′ | α - 1 y ′ ) ′ + q ( t ) | y | α - 1 y = 0 .