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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 \[ \bigl(p(t)|y'|^{\alpha-1}y'\bigr)'+q (t)|y|^{\alpha-1}y=0. \]

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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