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A stability problem with algebraic aspects

Published online by Cambridge University Press:  14 November 2011

F. V. Atkinson
F. V. Atkinson
Affiliation:
University of Toronto
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Synopsis

We consider the set S(f) of λ-values for which there exists a function g ∊ L(t0, ∞) such that

has a solution not tending to 0; here f is a fixed function which is positive, non-decreasing and tends to ∞ with t. It is shown that if the jumps of logf(t) at its discontinuities are uniformly bounded, then S(f) is an additive group. This group is determined in some cases; some related groups are noted, which may coincide with S(f).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 3-4 , 1978 , pp. 299 - 314
Copyright
Copyright © Royal Society of Edinburgh 1978

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