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

TitleMulti-interval Sturm–Liouville boundary-value problems with distributional potentials
Publication TypeJournal Article
Year of Publication2014
AuthorsGoriunov, AS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.07.043
Issue7
SectionMathematics
Pagination43-47
Date Published7/2014
LanguageEnglish
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.

Keywordsdistributional potentials, Sturm–Liouville problems
References: 

1. 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
2. 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
3. Sokolov M. S. Electron. J. Differential Equations, 2003, No. 75: 1–6.
4. Sokolov M. S. Rocky Mountain J. Math., 2006, 36, No. 2: 721–739. https://doi.org/10.1216/rmjm/1181069476
5. Zettl A. Rocky Mountain J. Math., 1975, 5, No. 3: 453–474. https://doi.org/10.1216/RMJ-1975-5-3-453
6. Everitt W. N., Markus L. Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators. Providence, RI: Amer. Math. Soc., 1999.
7. Zettl A. Sturm–Liouville theory. Providence, RI: Amer. Math. Soc., 2005.
8. Naimark M. A. Linear differential operators. Part 2. New York: F. Ungar, 1968. (Rus. ed.: Nauka, Moscow, 1969).
9. 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
10. Kochubei A. N. Mat. Zametki, 1979, 25, No. 3: 425–434.
11. Goriunov A. S., Mikhailets V. A. Meth. Funct. Anal. Topol., 2010, 16, No. 2: 120–130.