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An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

Alexey Fedoseev (2013)

Open Mathematics

We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.

An oscillatory half-linear differential equation

Árpád Elbert, Takaŝi Kusano, Tomoyuki Tanigawa (1997)

Archivum Mathematicum

A second-order half-linear ordinary differential equation of the type ( | y ' | α - 1 y ' ) ' + α q ( t ) | y | α - 1 y = 0 ( 1 ) is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.

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