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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