A first-order system of equations on a compact star graph
Abstract
This study concerns a boundary value problem generated by a system of first-order differential equations and some symmetric boundary conditions on a compact star graph. Unlike usual quantum graph Hamiltonians, the Hamiltonian considered in this paper acts on vector-valued functions living on the edges. Appropriate vertex conditions are introduced to ensure the corresponding boundary value problem is symmetric. In particular, coupling and separated conditions are imposed at the central and boundary vertices, respectively. Moreover, the general form of the vertex conditions at the central vertex is discussed. Finally, the characteristic function is constructed for the symmetric boundary value problem generated by the first-order system and specific coupling vertex conditions.
Keywords
References
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Details
Primary Language
English
Subjects
Ordinary Differential Equations, Difference Equations and Dynamical Systems, Operator Algebras and Functional Analysis
Journal Section
Research Article
Publication Date
December 24, 2025
Submission Date
January 3, 2025
Acceptance Date
June 18, 2025
Published in Issue
Year 2025 Volume: 74 Number: 4
APA
Mutlu, G., & Uğurlu, E. (2025). A first-order system of equations on a compact star graph. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(4), 751-758. https://doi.org/10.31801/cfsuasmas.1612785
AMA
1.Mutlu G, Uğurlu E. A first-order system of equations on a compact star graph. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74(4):751-758. doi:10.31801/cfsuasmas.1612785
Chicago
Mutlu, Gökhan, and Ekin Uğurlu. 2025. “A First-Order System of Equations on a Compact Star Graph”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 (4): 751-58. https://doi.org/10.31801/cfsuasmas.1612785.
EndNote
Mutlu G, Uğurlu E (December 1, 2025) A first-order system of equations on a compact star graph. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 4 751–758.
IEEE
[1]G. Mutlu and E. Uğurlu, “A first-order system of equations on a compact star graph”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 4, pp. 751–758, Dec. 2025, doi: 10.31801/cfsuasmas.1612785.
ISNAD
Mutlu, Gökhan - Uğurlu, Ekin. “A First-Order System of Equations on a Compact Star Graph”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/4 (December 1, 2025): 751-758. https://doi.org/10.31801/cfsuasmas.1612785.
JAMA
1.Mutlu G, Uğurlu E. A first-order system of equations on a compact star graph. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74:751–758.
MLA
Mutlu, Gökhan, and Ekin Uğurlu. “A First-Order System of Equations on a Compact Star Graph”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 4, Dec. 2025, pp. 751-8, doi:10.31801/cfsuasmas.1612785.
Vancouver
1.Gökhan Mutlu, Ekin Uğurlu. A first-order system of equations on a compact star graph. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025 Dec. 1;74(4):751-8. doi:10.31801/cfsuasmas.1612785
