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Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 2, Pages 9–16 (Mi ivm8866)  

This article is cited in 17 scientific papers (total in 17 papers)

Laplace operator with $\delta$-like potentials

B. E. Kanguzhina, D. B. Nurakhmetova, N. E. Tokmagambetovb

a Chair of Fundamental Mathematics, al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty, 500040 Republic of Kazakhstan
b Institute of Mathematics and Mathematical Modelling MES RK, 28 Shevchenko str., Almaty, 500012 Republic of Kazakhstan

Abstract: We study the Laplace operator in a punctured domain in a Hilbert space. We obtain an analog of the Green formula and a class of self-adjoint extensions of the Laplacian. We also investigate a certain class of well-posed problems.

Keywords: Laplace operator, punctured domain, analog of the Green formula, self-adjoint extension, well-posed problem.

Full text: PDF file (190 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:2, 6–12

UDC: 517.95
Received: 12.10.2012

Citation: B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Laplace operator with $\delta$-like potentials”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 2, 9–16; Russian Math. (Iz. VUZ), 58:2 (2014), 6–12

Citation in format AMSBIB
\Bibitem{KanNurTok14}
\by B.~E.~Kanguzhin, D.~B.~Nurakhmetov, N.~E.~Tokmagambetov
\paper Laplace operator with $\delta$-like potentials
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 2
\pages 9--16
\mathnet{http://mi.mathnet.ru/ivm8866}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 2
\pages 6--12
\crossref{https://doi.org/10.3103/S1066369X14020029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897814389}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. E. Akhymbek, D. B. Nurakhmetov, “Pervyi regulyarizovannyi sled operatora dvukratnogo differentsirovaniya na prokolotom otrezke”, Sib. elektron. matem. izv., 11 (2014), 626–633  mathnet
    2. Kanguzhin B.E., Tokmagambetov N.E., “a Regularized Trace Formula For a Well-Perturbed Laplace Operator”, Dokl. Math., 91:1 (2015), 1–4  crossref  mathscinet  zmath  isi  scopus
    3. B. E. Kanguzhin, N. E. Tokmagambetov, “Resolvents of well-posed problems for finite-rank perturbations of the polyharmonic operator in a punctured domain”, Siberian Math. J., 57:2 (2016), 265–273  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. A. Sarsenbi, L. K. Zhumanova, “First regularized trace of integro-differential Sturm-Liouville operator on a segment with punctured points at generalized conditions of bonding in deleted points”, Applications of Mathematics in Engineering and Economics, AMEE'16, AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040009  crossref  isi
    5. A. Sh. Aimakhanova, S. Kh. Shalginbayeva, L. K. Zhumanova, “The first regularized trace of integro-differential Sturm-Liouville operator on the segment with punctured points at integral perturbation of transmission conditions”, International Conference on Analysis and Applied Mathematics ICAAM 2016, AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020034  crossref  isi
    6. B. Kanguzhin, G. Nalzhupbayeva, “On identities for eigenvalues of a well-posed perturbation of the Laplace operator in a punctured domain”, International Conference on Analysis and Applied Mathematics ICAAM 2016, AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020092  crossref  isi
    7. M. Ruzhansky, N. Tokmagambetov, “Nonharmonic analysis of boundary value problems”, Int. Math. Res. Notices, 2016, no. 12, 3548–3615  crossref  isi
    8. B. E. Kanguzhin, D. Dauitbek, “A maximum of the first eigenvalue of semibounded differential operator with a parameter”, Russian Math. (Iz. VUZ), 61:2 (2017), 10–16  mathnet  crossref  isi
    9. Ya. Li, X. Li, X. Liu, “A fast and efficient hash function based on generalized chaotic mapping with variable parameters”, Neural Comput. Appl., 28:6, SI (2017), 1405–1415  crossref  isi  scopus
    10. G. Nalzhupbayeva, “Formulas for the eigenvalues of the iterated Laplacian with singular potentials”, International Conference Functional Analysis in Interdisciplinary Applications FAIA 2017, AIP Conf. Proc., 1880, eds. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 050005  crossref  isi  scopus
    11. G. Nalzhupbayeva, “Remark on the eigenvalues of the $m$-Laplacian in a punctured domain”, Complex Anal. Oper. Theory, 12:3 (2018), 599–606  crossref  mathscinet  zmath  isi  scopus
    12. G. Nalzhupbayeva, “Spectral properties of the iterated Laplacian with a potential in a punctured domain”, Filomat, 32:8 (2018), 2897–2900  crossref  mathscinet  isi  scopus
    13. G. Nalzhupbayeva, “Spectral properties of one elliptic operator in a punctured domain”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, eds. A. Ashyralyev, A. Lukashov, M. Sadybekov, Amer. Inst. Phys., 2018, 020083-1  crossref  isi  scopus
    14. N. F. Valeev, E. A. Nazirova, “Pryamaya i obratnaya spektralnye zadachi v teorii kolebanii uprugoi plastiny s dopolnitelnymi tochechnymi vzaimodeistviyami”, Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 152, VINITI RAN, M., 2018, 25–33  mathnet  mathscinet
    15. Valeev N.F., Nazirova E.A., Azizova R.G., “Multiparameter Inverse Spectral Problems in the Oscillation Model of An Orthotropic Plate”, Azerbaijan J. Math., 9:2 (2019), 88–99  isi
    16. G. E. Abduakhitova, B. E. Kanguzhin, “Korrektnoe opredelenie ellipticheskikh operatorov vtorogo poryadka s tochechnymi vzaimodeistviyami i ikh rezolventy”, Matem. tr., 23:1 (2020), 3–15  mathnet  crossref
    17. Kanguzhin B.E., Tulenov K.S., “Singular Perturbations of Laplace Operator and Their Resolvents”, Complex Var. Elliptic Equ., 65:9 (2020), 1433–1444  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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