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Mat. Zametki, 1996, Volume 60, Issue 3, Pages 468–470 (Mi mz1853)  

This article is cited in 20 scientific papers (total in 20 papers)

Brief Communications

Oscillation properties of the spectrum of a boundary value problem on a graph

Yu. V. Pokornyi, V. L. Pryadiev, A. Al-Obeid

Voronezh State University


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English version:
Mathematical Notes, 1996, 60:3, 351–353

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Received: 13.12.1994

Citation: Yu. V. Pokornyi, V. L. Pryadiev, A. Al-Obeid, “Oscillation properties of the spectrum of a boundary value problem on a graph”, Mat. Zametki, 60:3 (1996), 468–470; Math. Notes, 60:3 (1996), 351–353

Citation in format AMSBIB
\by Yu.~V.~Pokornyi, V.~L.~Pryadiev, A.~Al-Obeid
\paper Oscillation properties of the spectrum of a~boundary value problem on a~graph
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 3
\pages 468--470
\jour Math. Notes
\yr 1996
\vol 60
\issue 3
\pages 351--353

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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. Pokornyi, YV, “A nonlinear boundary value problem on a graph”, Differential Equations, 34:5 (1998), 631  mathnet  mathscinet  zmath  isi
    2. Kamenskii, MI, “On the semigroup in the diffusion problem on the network”, Doklady Akademii Nauk, 368:2 (1999), 157  mathnet  mathscinet  isi
    3. Pokornyi, YV, “Nonoscillation of ordinary differential equations and inequalities on spatial networks”, Differential Equations, 37:5 (2001), 695  mathnet  crossref  mathscinet  isi  scopus  scopus
    4. Yu. V. Pokornyi, V. L. Pryadiev, “Some problems of the qualitative Sturm–Liouville theory on a spatial network”, Russian Math. Surveys, 59:3 (2004), 515–552  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Oren, I, “Nodal domain counts and the chromatic number of graphs”, Journal of Physics A-Mathematical and Theoretical, 40:32 (2007), 9825  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Berkolaiko, G, “A lower bound for nodal count on discrete and metric graphs”, Communications in Mathematical Physics, 278:3 (2008), 803  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Band R., Oren I., Smilansky U., “Nodal Domains on Graphs - How to Count Them and Why?”, Analysis on Graphs and its Applications, Proceedings of Symposia in Pure Mathematics, 77, eds. Exner P., Keating J., Kuchment P., Sunada T., Teplyaev A., Amer Mathematical Soc, 2008, 5–27  crossref  mathscinet  zmath  isi
    8. Wang L., Xu G.Q., Mastorakis N.E., “Inverse Problem of Networks-Reconstruction of Graph”, New Aspects of Systems Theory and Scientific Computation, Mathematics and Computers in Science and Engineering, eds. Mastorakis N., Mladenov V., Bojkovic Z., World Scientific and Engineering Acad and Soc, 2010, 41–47  mathscinet  isi
    9. Band R., Berkolaiko G., Raz H., Smilansky U., “The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions”, Commun. Math. Phys., 311:3 (2012), 815–838  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Berkolaiko G., Kuchment P., “Dependence of the Spectrum of a Quantum Graph on Vertex Conditions and Edge Lengths”, Spectral Geometry, Proceedings of Symposia in Pure Mathematics, 84, eds. Barnett A., Gordon C., Perry P., Uribe A., Amer Mathematical Soc, 2012, 117–137  crossref  mathscinet  zmath  isi
    11. Band R., Berkolaiko G., Smilansky U., “Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs”, Ann. Henri Poincare, 13:1 (2012), 145–184  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. Band R., “The Nodal Count (0,1,2,3,...) Implies the Graph Is a Tree”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 372:2007 (2014), 20120504  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Berkolaiko G., Weyand T., “Stability of Eigenvalues of Quantum Graphs With Respect To Magnetic Perturbation and the Nodal Count of the Eigenfunctions”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 372:2007 (2014), 20120522  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Band R., Berkolaiko G., Weyand T., “Anomalous Nodal Count and Singularities in the Dispersion Relation of Honeycomb Graphs”, J. Math. Phys., 56:12 (2015), 122111  crossref  mathscinet  zmath  isi  scopus  scopus
    15. L. K. Zhapsarbayeva, B. E. Kanguzhin, M. N. Konyrkulzhayeva, “Self-adjoint restrictions of maximal operator on graph”, Ufa Math. J., 9:4 (2017), 35–43  mathnet  crossref  isi  elib
    16. Berkolaiko G., “An Elementary Introduction to Quantum Graphs”, Geometric and Computational Spectral Theory, Contemporary Mathematics, 700, eds. Girouard A., Jakobson D., Levitin M., Nigam N., Polterovich I., Rochon F., Amer Mathematical Soc, 2017, 41–72  crossref  mathscinet  zmath  isi  scopus  scopus
    17. Berkolaiko G., Kennedy J.B., Kurasov P., Mugnolo D., “Edge Connectivity and the Spectral Gap of Combinatorial and Quantum Graphs”, J. Phys. A-Math. Theor., 50:36 (2017), 365201  crossref  mathscinet  zmath  isi  scopus  scopus
    18. Alon L., Band R., Berkolaiko G., “Nodal Statistics on Quantum Graphs”, Commun. Math. Phys., 362:3 (2018), 909–948  crossref  mathscinet  zmath  isi  scopus
    19. Band R., Krueger A.J., “Nonlinear Sturm Oscillation: From the Interval to a Star”, Mathematical Problems in Quantum Physics, Contemporary Mathematics, 717, eds. Bonetto F., Borthwick D., Harrell E., Loss M., Amer Mathematical Soc, 2018, 129–154  crossref  mathscinet  isi  scopus
    20. Band R., Gnutzmann S., Krueger A.J., “On the Nodal Structure of Nonlinear Stationary Waves on Star Graphs”, Symmetry-Basel, 11:2 (2019), 185  crossref  mathscinet  isi  scopus
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