Abstract
In this article, a discontinuous Sturm–Liouville boundary value problem with non-separated boundary conditions is considered. It is proven that the potential function is uniquely established by either the Weyl function or by two spectra.
Similar content being viewed by others
References
Ambartsumyan VA (1929) Uber Eine Frage Der Eigenwerttheorie. Z Phys 53:690–695
Buterin SA, Shieh CT (2009) Inverse nodal problems for differential pencils. Appl Math Lett 22(8):1240–1247
Conway JB (1995) Functions of one complex variable. Springer, New York
Freiling G, Yurko VA (2001) Inverse Sturm–Liouville problems and their applications. NOVA Science Publisher, New York
Freiling G, Yurko VA (2010) Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter. Inverse Probl 26:055003
Gou K, Chen Z (2015) Inverse Sturm–Liouville problems and their biomedical engineering applications. JSM Math Stat 2(1):1008
Gou K, Joshi S, Walton JR (2012) Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique. Int J Eng Sci 56:1–16
Hald OH (1984) Discontinuous inverse eigenvalue problems. Commun Pure Appl Math 37:539–577
Khalili Y, Dabbaghian A, Khaleghi Moghadam M (2018) Uniqueness of inverse problems for differential pencils with the spectral discontinuity condition. Univ Politeh Bucharest Sci Bull Ser A Appl Math Phys 80:207–218
Koyunbakan H (2011) Inverse problem for a quadratic pencil of Sturm–Liouville operator. J Math Anal Appl 378:549–554
Krueger RJ (1982) Inverse problems for nonabsorbing media with discontinuous material properties. J Math Phys 23(3):396–404
Litvinenko ON, Soshnikov VI (1964) The theory of heterogeneous lines and their applications in radio engineering. Radio, Moscow
Mennicken R, Möller M (2003) Non-self-adjoint boundary eigenvalue problems. North-Holland Mathematic Studies. North-Holland, Amsterdam
Meschanov VP, Feldstein AL (1980) Automatic design of directional couplers. Sviaz, Moscow
Neamaty A, Khalili Y (2014) The uniqueness theorem for differential pencil with jump condition in the finite interval. Iran J Sci Technol 38(A3):305–309
Pivovarchik V (2012) On the Hald–Gesztesy–Simon theorem. Integr Equ Oper Theory 73:383–393
Shieh CT, Yurko VA (2008) Inverse nodal and inverse spectral problems for discontinuous boundary value problems. J Math Anal Appl 347:266–272
Wang YP (2015) Inverse problems for discontinuous Sturm-Liouville operators with mixed spectral data. Inverse Probl Sci Eng 23:1180–1198
Wang YP, Yurko VA (2016) On the inverse nodal problems for discontinuous Sturm–Liouville operators. J Differ Equ 260:4086–4109
Yurko VA (2000) Integral transforms connected with discontinuous boundary value problems. Integral Transforms Spec Funct 10:141–164
Yurko V (2012) Inverse problems for non-selfadjoint quasi-periodic differential pencils. Anal Math Phys 2(3):215–230
Yurko VA (2016) Inverse problem for quasi-periodic differential pencils with jump conditions inside the interval. Complex Anal Oper Theory 10(6):1203–1212
Zhdanovich VF (1960) Formulae for the zeros of Dirichlet polynomials and quasi-polynomials. Dokl Acad Nauk SSSR 135(8):1046–1049
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Khalili, Y., Kadkhoda, N. An Inverse Problem for Discontinuous Sturm–Liouville Equations with Non-separated Boundary Conditions. Iran J Sci Technol Trans Sci 44, 493–496 (2020). https://doi.org/10.1007/s40995-020-00854-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40995-020-00854-y