Distribution of eigenvalues of the Sturm-Liouville problem with slowly increasing potential
Abstract
We establish an asymptotic representation of the function ˜n(R)=R∫0n(r)−n(0)rdr,R∈ℜ⊆[0,∞),R→∞, 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∈ℜ .
Published
25.06.1996
How to Cite
Palyutkin, V. G. “Distribution of Eigenvalues of the Sturm-Liouville Problem With Slowly Increasing Potential”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 6, June 1996, pp. 813-25, https://umj.imath.kiev.ua/index.php/umj/article/view/5281.
Issue
Section
Research articles