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let / = /(t) denote a real-valued, continuous function on the half-line 0 ^ t < ». Both necessary and sufficient conditions in order that the equation (1) be oscillatory, so that every solution of (1) possesses an infinity of zeros on 0 t < =» clustering at + co t are known; see, for instance, [10], [5]. The present note will deal primarily with the problem of obtaining a sufficient criterion in order that (1) be oscillatory, in the particular case that f{t) satisfies the limit relation

A sufficient condition for an infinite discrete spectrum