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Peer-reviewedCC BY 4.0Mathematics

Fourth-Order Finite Spectrum Problems on Time Scales with Finitely Many Interior Nodes

  • Bayram Bala1
  1. 1Department of Fundamental Sciences, Faculty of Engineering and Natural Sciences, Gaziantep Islam Science and Technology University, 27010 Gaziantep, Türkiye
Open at sourceDOICite

Abstract

In this paper, we investigate fourth-order boundary value problems with finite spectrum on hybrid time scales containing finitely many isolated interior nodes. Under fourth-order Atkinson-type conditions, we construct the global transfer matrix and show that the corresponding characteristic function is a polynomial in the spectral parameter. Consequently, the problem has only finitely many eigenvalues. An explicit upper bound for their number is also obtained in terms of the partition parameters of the continuous components and the number of isolated interior nodes. The results extend finite-spectrum theory to higher-order dynamic equations on hybrid time scales and clarify the spectral contribution of the interior nodes.

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Cite

BibTeXRIS
BibTeX
@article{bala2026fourthorder,
  title = {{Fourth-Order Finite Spectrum Problems on Time Scales with Finitely Many Interior Nodes}},
  author = {Bayram Bala},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203643},
  url = {https://www.mdpi.com/2227-7390/14/20/3643},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Fourth-Order Finite Spectrum Problems on Time Scales with Finitely Many Interior Nodes
AU  - Bayram Bala
PY  - 2026
DA  - 2026/10/09
JO  - Mathematics
DO  - 10.3390/math14203643
UR  - https://www.mdpi.com/2227-7390/14/20/3643
AB  - In this paper, we investigate fourth-order boundary value problems with finite spectrum on hybrid time scales containing finitely many isolated interior nodes. Under fourth-order Atkinson-type conditions, we construct the global transfer matrix and show that the corresponding characteristic function is a polynomial in the spectral parameter. Consequently, the problem has only finitely many eigenvalues. An explicit upper bound for their number is also obtained in terms of the partition parameters of the continuous components and the number of isolated interior nodes. The results extend finite-spectrum theory to higher-order dynamic equations on hybrid time scales and clarify the spectral contribution of the interior nodes.
SN  - 2227-7390
ER  -