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Nonoscillatory half-linear differential equations and generalized Karamata functions. (English) Zbl 1103.34017

Summary: 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

p(t)| y ' | α-1 y ' ' +q(t)|y| α-1 y=0·

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory