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 typeequation(A)(p(t)|y′|α-1y′)′+q(t)|y|α-1y=0.(p(t)|y′|α-1y′)′+q(t)|y|α-1y=0.