Geodesic
Systems of differential equations on the line with regular singularities
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 27-31 
O. B. Gorbunov; C.-T. Shieh; V. A. Yurko. Systems of differential equations on the line with regular singularities. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 27-31. http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Non-selfadjoint second order differential systems on the line having a non-integrable regular singularity are studied. We construct special fundamental systems of solutions with prescribed analytic and asymptotic properties. Asymptotics of the corresponding Stockes multipliers is established.

[1] Naimark M. A., Linear Differential Operators, v. I, Ungar, New York, 1967; v. II, 1968; Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

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

[3] Litvinenko O. N., Soshnikov V. I., The Theory of Heterogenious Lines and their Applications in Radio Engineering, Radio, M., 1964 (in Russian)

[4] Freiling G., Yurko V. A., “Reconstructing parameters of a medium from incomplete spectral information”, Results. Math., 35:3–4 (1999), 228–249 | DOI

[5] Lapwood F. R., Usami T., Free Oscilations of the Earth, Cambridge University Press, Cambridge, 1981

[6] Gasymov M. G., “Determination of Sturm–Liouville equation with a singular point from two spectra”, Sov. Math. Dokl., 6 (1965), 396–399

[7] Yurko V. A., “Inverse problem for differential equations with a singularity”, Differ. Equations, 28 (1992), 1100–1107

[8] Yurko V. A., “On higher-order differential operators with a regular singularity”, Sb. Math., 186:6 (1995), 901–928 | DOI

[9] Yurko V. A., “Integral transforms connected with differential operators having singularities inside the interval”, Integral Transforms and Special Functions, 5:3–4 (1997), 309–322 | DOI

[10] Gorbunov O., Shieh C.-T., Yurko V., Spectral analysis of the Dirac system with a singularity in an interior point, 17 pp., arXiv: 1410.2020v1 [math.SP]