Half inverse problems for the impulsive singular diffusion operator

Year 2020, Volume: 5 Issue: 3, 186 - 198, 30.12.2020

Rauf Amirov , Abdullah Ergün

Abstract

In this paper, we consider the inverse spectral problem for the impulsive
Sturm-Liouville differential pencils on $\left[ 0,\pi\right] $ with the
Robin boundary conditions and the jump conditions at the point $\dfrac{\pi}%
{2}$. We prove that two potentials functious on the whole interval and the
parameters in the boundary and jump conditions can be determined from a set of
eigenvalues for two cases: (i) The potentials is given on $\left(
0,\dfrac{\pi}{4}\left( \alpha+\beta \right) \right) .$ (ii) The potentials is
given on $\left( \alpha+\beta, \dfrac{\alpha+\beta}{2} \right) $, where
$0<\alpha+\beta<1$, $\alpha+\beta>1$ respectively. Finally, was given interior inverse problem for same boundary problem.

Keywords

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

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