Recovering differential pencils on graphs with a cycle from spectra

Article Sidebar

PDF Recovering Differential Pencils on Graphs with a Cycle from Spectra
Published: Jun 30, 2014
DOI: https://doi.org/10.5556/j.tkjm.45.2014.1492
Keywords:
geometrical graphs with a cycle differential pencils inverse spectral problems

Main Article Content

Vjacheslav Anatoljevich Yurko
Professor

Abstract

We study boundary value problems on compact graphs with a cycle for second-order ordinary differential equations with nonlinear dependence on the spectral parameter. We establish properties of the spectral characteristics and investigate inverse spectral problems of recovering coefficients of the differential equation from spectra. For these inverse problems we prove uniqueness theorems and provide procedures for constructing their solutions.

Article Details

How to Cite
Yurko, V. A. (2014). Recovering differential pencils on graphs with a cycle from spectra. Tamkang Journal of Mathematics, 45(2), 195–206. https://doi.org/10.5556/j.tkjm.45.2014.1492
Issue
Vol. 45 No. 2 (2014)
Section
Papers
Author Biography

Vjacheslav Anatoljevich Yurko, Professor

Department of Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia

References

V. A. Marchenko, Sturm-Liouville operators and their applications, Naukova Dumka, Kiev, 1977; English transl., Birkhauser, 1986.

B. M. Levitan, Inverse Sturm-Liouville problems, Nauka, Moscow, 1984; English transl., VNU Sci.Press, Utrecht, 1987.

R. Beals, P. Deift and C. Tomei, Direct and Inverse Scattering on the Line, Math. Surveys and Monographs, v.28. Amer. Math. Soc. Providence: RI, 1988.

G. Freiling and V. A. Yurko, Inverse Sturm-Liouville Problems and their Applications, NOVA Science Publishers, New York, 2001.

V. A. Yurko, Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series. VSP, Utrecht, 2002.

Yu. V. Pokornyi and A. V. Borovskikh, Differential equations on networks $($geometric graphs$)$, J. Math. Sci. (N.Y.), 119, no.6 (2004), 691--718.

Yu. Pokornyi and V. Pryadiev, The qualitative Sturm-Liouville theory on spatial networks, J. Math. Sci. (N.Y.), 119(2004), %no.6, 788--835.

M. I. Belishev, Boundary spectral inverse problem on a class of graphs $($trees$)$ by the BC method, Inverse Problems, 20(2004), 647--672.

V. A. Yurko, Inverse spectral problems for Sturm-Liouville operators on graphs, Inverse Problems, 21(2005), 1075--1086.

B. M. Brown and R. Weikard, A Borg-Levinson theorem for trees, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461, no.2062 (2005), 3231--3243.

V. A. Yurko, Inverse problems for Sturm-Liouville operators on bush-type graphs, Inverse Problems, 25, no.10 (2009), 105008, 14pp.

V. A. Yurko, Inverse spectral problems for differential operators on a graph with a rooted cycle, Tamkang Journal of Mathematics, 40, no.3 (2009), 271--286.

V. A. Yurko, An inverse problem for Sturm-Liouville operators on A-graphs,Applied Math. Letters, 23, no.8(2010), 875--879.

V. A. Yurko, Inverse spectral problems for differential operators on arbitrary compact graphs, Journal of Inverse and Ill-Posed Proplems, 18, no.3 (2010), 245--261.

V. A. Yurko, Recovering differential pencils on compact graphs, J. Differ. Equations, 244(2008), 431--443.

V. A. Yurko, Inverse problems for non-selfadjoint quasi-periodic differential pencils, Analysis and Math. Physics, 2, no.3(2012), 215--230.

M. A. Naimark, Linear Differential Operators, 2nd ed., Nauka, Moscow, 1969; English transl. of 1st ed., Parts I,II, Ungar, New York, 1967, 1968.

V. A. Yurko, Differential pensils on graphs with a cycle, Schriftenreiche des

Fachbereichs Mathematik, SM-DUE-758, Universitaet Duisburg-Essen, 2013, 12pp.

Most read articles by the same author(s)