A stability problem with algebraic aspects

Abstract

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