The equation y″ + [λ - q(x)]y = 0 on (0, ∞) or (-∞, ∞), in which q(x) → ∞ as x → ∞ or x → ± ∞, has a complete set of eigenfunctions with discrete eigenvalues {λn}n=0∞. We derive an inequality that contains λn, by using a quick and elementary method that does not employ a comparison theorem or assume anything special. Explicit lower bounds for λn can often be easily obtained, and three examples are given. The method also gives respectable lower bounds for λn in the classical Sturm—Liouville case.
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机译：在（0，∞）或（-∞，∞）上等式y''+ [λ-q（x）] y = 0，其中q（x）→∞为x→∞或x→±∞，具有具有离散特征值{λn} n = 0 ∞的完整特征函数集。我们通过使用一种不采用比较定理或假设特殊条件的快速基本方法来得出包含λn的不等式。可以很容易地获得λn的明确下界，并给出了三个示例。在经典Sturm-Liouville情况下，该方法还给出了λn的合理下界。
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