Asymptotics of the solutions of the Sturm–Liouville equation with singular coefficients

Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients

“…The matrix-function F (x) is the special case of the regularization matrix by Mirzoev and Shkalikov [1]. It coincides with the associated matrices from [46] and [47]. For T ∈ T 0 2 (i.e.…”

Wave equation for Sturm-Liouville operator with singular potentials

“…In the paper of Savchuk and Shkalikov [19], asymptotic estimates of the eigenvalues and eigenfunctions of the Sturm-Liouville operator with singular potentials were obtained. This method was later developed in the works of [12], [18], [20], [21]. To apply the concept of very weak solutions to our problem, we will first consider cases where the potentials of the Sturm-Liouville operator are more regular.…”

“…Savchuk and Shkalikov's study in [18] yielded eigenvalues and eigenfunctions for this operator. Additionally, studies in [12], [17], [19], and [20] explored the Sturm-Liouville operator with potential-distributions. To establish the framework for very weak solutions, our focus is primarily on estimating solutions for more regular problems while also considering the impact of a regularization parameter on these solutions.…”

Wave equation for Sturm-Liouville operator with singular potentials

“…By Savchuk and Shkalikov, in [14], eigenvalues and eigenfunctions for the Sturm-Liouville operator with singular potentials were obtained. Also in [10], [13], [15], [16] one studied the Sturm-Liouville operator with potential-distributions. In order to set up the machinery of very weak solutions, here we are rather interested in estimates for solutions of more regular problems, keeping track of a more explicit dependence on the regularisation parameter.…”