Abstract
Dorodnitsyn suggested [1] a method for calculating approximately eigenvalues of Sturm–Liouville boundary value problems with a spectral parameter λ : y′′ + (λr(x) + q(x))y = 0, 0 ≤ x ≤ `, h1y(0) = hy(0), H1y(`) +Hy(`) = 0. (1) Here the function q(x) is assumed to be continuous and real-valued over the closed interval [0, `]; h, h1, H, H1 ∈ R, and the coefficient r(x) has the form r(x) = r1(x)x, where α > −1, and r1(x) is a continuous positive function on [0, `]. In this situation, eigenvalues of problem (1) form a strictly increasing sequence {λn}n=1 with the asymptotic √ λn ∼ πn / ` ∫
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