Multi-interval Sturm–Liouville boundary-value problems with distributional potentials

Authors

  • A. S. Goriunov

DOI:

https://doi.org/10.15407/dopovidi2014.07.043

Keywords:

distributional potentials, Sturm–Liouville problems

Abstract

We study the multi-interval boundary-value Sturm–Liouville problems with distributional potentials. For the corresponding symmetric operators boundary triplets are found and the constructive descriptions of all self-adjoint, maximal dissipative and maximal accumulative extensions and generalized resolvents in terms of homogeneous boundary conditions are given. It is shown that all real maximal dissipative and maximal accumulative extensions are self-adjoint and all such extensions are described.

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References

Everitt W. N., Zettl A. Rocky Mountain J. Math., 1986, 16, No. 3: 497–516. https://doi.org/10.1216/RMJ-1986-16-3-497

Everitt W. N., Zettl A. Proc. London Math. Soc., 1992, 64, No. 3: 524–544. https://doi.org/10.1112/plms/s3-64.3.524

Sokolov M. S. Electron. J. Differential Equations, 2003, No. 75: 1–6.

Sokolov M. S. Rocky Mountain J. Math., 2006, 36, No. 2: 721–739. https://doi.org/10.1216/rmjm/1181069476

Zettl A. Rocky Mountain J. Math., 1975, 5, No. 3: 453–474. https://doi.org/10.1216/RMJ-1975-5-3-453

Everitt W. N., Markus L. Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators. Providence, RI: Amer. Math. Soc., 1999.

Zettl A. Sturm–Liouville theory. Providence, RI: Amer. Math. Soc., 2005.

Naimark M. A. Linear differential operators. Part 2. New York: F. Ungar, 1968. (Rus. ed.: Nauka, Moscow, 1969).

Gorbachuk V. I., Gorbachuk M. L. Boundary value problems for operator differential equations. Dordrecht: Kluwer, 1991. (Rus. ed.: Naukova Dumka, Kiev, 1984). https://doi.org/10.1007/978-94-011-3714-0

Kochubei A. N. Mat. Zametki, 1979, 25, No. 3: 425–434.

Goriunov A. S., Mikhailets V. A. Meth. Funct. Anal. Topol., 2010, 16, No. 2: 120–130.

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Published

28.02.2025

How to Cite

Goriunov, A. S. (2025). Multi-interval Sturm–Liouville boundary-value problems with distributional potentials . Reports of the National Academy of Sciences of Ukraine, (7), 43–47. https://doi.org/10.15407/dopovidi2014.07.043