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Asymptotically uniform functions: a single hypothesis which solves two old problems
Abstract The asymptotic study of a time-dependent function ƒ as the solution of a differential equation often leads to the question of whether its derivative $$f'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> vanishes at infinity. We show that a necessary and sufficient condition for this is that $$f'$$ <mml:math …