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

equation(A)

(p(t)|y^′|^α-1y^′)^′+q(t)|y|^α-1y=0.$(p(t)|y^{\prime }{|}^{\alpha -1}{y}^{\prime }{)}^{\prime }+q(t)|y{|}^{\alpha -1}y=0\text{.}$