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Slowly varying solutions of second-order linear differential equations. (English) Zbl 0965.34044

The author investigates the asymptotic behavior for \(x\to \infty\) of slowly varying solutions \(y(x)\) (in the sense of Karamata) to the equation \[ y''-f(x)y(x)=0. \] The results are determined under less restrictive conditions than known before.

MSC:

34E05 Asymptotic expansions of solutions to ordinary differential equations
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
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