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We find the asymptotics as λ/ɛ → −∞ of the density of the spectral measure of the Sturm-Liouville operator in L 2(0,+∞) generated by the expression −y″ + ɛq(x)y, ɛ > 0, with the boundary condition y(0) cos α+y′(0) sinα = 0. The potential q(x) tends to −∞ as x → +∞ and is assumed to satisfy the Sears condition and some additional regularity conditions.
Differential Equations – Springer Journals
Published: Jul 19, 2009
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