An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition

Chuan-Fu Yang; Natalia Pavlovna Bondarenko; Xiao-Chuan Xu

doi:10.3934/ipi.2019068

Article Contents

2020, Volume 14, Issue 1: 153-169. Doi: 10.3934/ipi.2019068

This issue Previous Article Factorization method for imaging a local perturbation in inhomogeneous periodic layers from far field measurements Next Article

An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition

1.
Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, Russia
3.
Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia
4.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

^* Corresponding author: Natalia Bondarenko
^* Corresponding author: Natalia Bondarenko

Received: June 2019

Published: November 2019

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Abstract

The Sturm-Liouville pencil is studied with arbitrary entire functions of the spectral parameter, contained in one of the boundary conditions. We solve the inverse problem, that consists in recovering the pencil coefficients from a part of the spectrum satisfying some conditions. Our main results are 1) uniqueness, 2) constructive solution, 3) local solvability and stability of the inverse problem. Our method is based on the reduction to the Sturm-Liouville problem without the spectral parameter in the boundary conditions. We use a special vector-functional Riesz-basis for that reduction.

Keywords:

Inverse spectral problems,
Strum-Liouville equation,
eigenparameter-dependent boundary conditions,
uniqueness,
constructive algorithm,
local solvability and stability.

Mathematics Subject Classification: 34A55, 34B07, 34B09, 34L40.

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References

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