Half Inverse Problems For The Impulsive Quadratic Pencil With The Discontinouty Coefficient

Authors

RAUF AMİROV
SEVİM DURAK

Abstract

In this paper, we study the inverse spectral problem for the quadratic differential pencils with discontinuity coefficient on $\left[ 0,\pi\right] $ with separable boundary conditions and the impulsive conditions at the point $x=\dfrac{\pi}{2}$. We prove that two potential functions on the interval $\left[ 0,\pi\right] $, and the parameters in the boundary and impulsive conditions can be determined from a sequence of eigenvalues for two cases: (i) The potentials are given on $\left( 0,\dfrac{\pi}{4}\left( 1+\alpha\right) \right) ,$ (ii) The potentials are given on $\left( \dfrac{\pi}{4}\left( 1+\alpha\right) ,\pi\right) $, where $0

DOI

10.3906/mat-2104-40

Keywords

Inverse spectral problems, Sturm--Liouville operator, spectrum, uniqueness

First Page

1847

Last Page

1870

Recommended Citation

AMİROV, RAUF and DURAK, SEVİM (2021) "Half Inverse Problems For The Impulsive Quadratic Pencil With The Discontinouty Coefficient," Turkish Journal of Mathematics: Vol. 45: No. 4, Article 27. https://doi.org/10.3906/mat-2104-40
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/27