Global two-sided Abel-type bounds on positive kernels do not force solutions of scaled Volterra equations to converge to zero, as shown by an explicit counterexample where a subsequence diverges.
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A counterexample to Abel-type asymptotics for scaled Volterra equations
Global two-sided Abel-type bounds on positive kernels do not force solutions of scaled Volterra equations to converge to zero, as shown by an explicit counterexample where a subsequence diverges.