International Journal of Nonlinear Analysis and Applications

Half inverse problems for the singular Sturm-Liouville operator

Document Type : Research Paper

Authors

Sivas Cumhuriyet University, Faculty of Science, Department of Mathematics, 58140, Turkey

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 functions 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 are given on $\left(0,\dfrac{\pi}{4}\left(  \alpha+\beta\right)  \right)  .$ (ii) The potentials is given on $\left(  \dfrac{\pi}{4}\left(  \alpha+\beta\right)  ,\dfrac{\pi }{2}\left(  \alpha+\beta\right)  \right)  $, where $0<\alpha<\beta<1$ and $\alpha+\beta>1$, respectively.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 3161-3171
  • Receive Date: 31 May 2022
  • Revise Date: 15 June 2022
  • Accept Date: 24 July 2022