2019
Том 71
№ 7

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Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential

Palyutkin V. G.

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Abstract

We establish an asymptotic representation of the function \(\tilde n(R) = \int\limits_0^R {\frac{{n(r) - n(0)}}{r}dr, R \in \Re } \subseteq [0, \infty ), R \to \infty ,\) where n(r) is the number of eigenvalues of the Sturm-Liouville problem on [0,∞) in (λ:¦λ¦≤r) (counting multiplicities). This result is obtained under assumption that q(x) slowly (not faster than In x) increases to infinity as x→∞ and satisfies additional requirements on some intervals \([x_ - (R), x_ + (R)],R \in \Re \) .

English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 6, pp 914-927.

Citation Example: Palyutkin V. G. Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential // Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 813-825.

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