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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some unbounded functions of regular growth
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by H. Arthur DeKleine and Vladimir Drobot
Proc. Amer. Math. Soc. 35 (1972), 471-476
DOI: https://doi.org/10.1090/S0002-9939-1972-0303025-2

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.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 471-476
  • MSC: Primary 34D05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0303025-2
  • MathSciNet review: 0303025