No abstract

The Jost solutions of the Schrödinger-type equation with a polynomial energy-dependent potential on the entire real line (−∞; + ∞) are investigated. The integral representations for the Jost solutions are constructed and some properties are studied.

In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.

No abstract

In the present paper the inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential is investigated on the entire real line (−∞; + ∞). The scattering data of the scattering problem are defined and the properties of the data are studied. The system of the main integral equations of the scattering problem is derived and the potential functions are recovered.

No abstract

No abstract

In this paper we have introduced the I-localized and the I^{∗}-localized sequences in metric spaces and investigate some basics properties of the I-localized sequences related with I-Cauchy sequences. Also we have obtained some necessary and sufficient conditions for the I-localized sequences to be an I-Cauchy sequences. It is also defined uniformly the I-localized sequences on metric spaces and its relation with I-Cauchy sequences has been  obtained.