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Lyapunov-Krasovsky Functionals and the Existence of Unbounded Solutions of Functional-Differential Equations of Retarded Type

  • Lapin K. S.
  • Lapin S. V
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Abstract

In this paper, the concepts of unboundedness and partial unboundedness of solutions of functional-differential equations of retarded type are introduced. On the basis of the method of Lyapunov-Krasovsky functionals, sufficient conditions for the existence of partially unbounded solutions are obtained. As corollaries, sufficient conditions for the existence of unbounded solutions are obtained.

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Cite

BibTeXRIS
BibTeX
@misc{k2026lyapunovkrasovsky,
  title = {{Lyapunov-Krasovsky Functionals and the Existence of Unbounded Solutions of Functional-Differential Equations of Retarded Type}},
  author = {Lapin K. S. and Lapin S. V},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24620},
  eprint = {2610.24620},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24620},
}
RIS
TY  - UNPB
TI  - Lyapunov-Krasovsky Functionals and the Existence of Unbounded Solutions of Functional-Differential Equations of Retarded Type
AU  - Lapin K. S.
AU  - Lapin S. V
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24620
UR  - https://arxiv.org/abs/2610.24620
AB  - In this paper, the concepts of unboundedness and partial unboundedness of solutions of functional-differential equations of retarded type are introduced. On the basis of the method of Lyapunov-Krasovsky functionals, sufficient conditions for the existence of partially unbounded solutions are obtained. As corollaries, sufficient conditions for the existence of unbounded solutions are obtained.
ER  -