Some unbounded functions of regular growth

DeKleine, H. Arthur; Drobot, Vladimir

doi:10.1090/S0002-9939-1972-0303025-2

Some unbounded functions of regular growth
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by H. Arthur DeKleine and Vladimir Drobot PDF

Proc. Amer. Math. Soc. 35 (1972), 471-476 Request permission

Abstract:

The concept of regular growth for unbounded nondecreasing functions has its origin in the study of the asymptotic behavior of solutions for the second order equation $u'' + a(t)u = 0$. In this paper we give sufficient conditions for a continuous, differentiable function $a(t)$ to possess the property that its logarithm increases regularly. We also show that the logarithm of a continuous unbounded concave or convex function increases regularly.

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