Project information
Oscillation theory on hybrid time domains with applications in spectral and matrix analysis
(Oscilační teorie na hybridních časových doménách)
- Project Identification
- GA23-05242S
- Project Period
- 1/2023 - 12/2025
- Investor / Pogramme / Project type
-
Czech Science Foundation
- Standard Projects
- MU Faculty or unit
- Faculty of Science
This project deals with the oscillation theory for differential equations on hybrid time domains, including the continuous and discrete time. The principal aim is to explain the nature of oscillations on hybrid time domains (also called time scales), being an open problem in the theory of differential equations. We propose new approach to this problem by the investigation of the comparative index, which is a relatively new notion from matrix analysis and which was originally developed for the study of discrete oscillations. We also aim to develop related problems from the spectral theory or variational analysis on discrete and hybrid time domains, where the existence or nonexistence of oscillations plays a fundamental role, such as in the study of self-adjoint extensions of linear relations, spectral counting functions, or the optimality conditions in nonlinear optimization problems. We will also develop new applications of the methods and techniques from the oscillation theory in matrix analysis and other related fields (e.g. the Maslov index).
Publications
Total number of publications: 3
2024
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Contributions to Generalized Oscillation Theory of Linear Hamiltonian Systems
Results in Mathematics, year: 2024, volume: 79, edition: 8, DOI
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Note on singular Sturm comparison theorem and strict majorant condition
Journal of Mathematical Analysis and Applications, year: 2024, volume: 538, edition: 2, DOI
2023
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Generalized focal points and local Sturmian theory for linear Hamiltonian systems
Discrete and Continuous Dynamical Systems, year: 2023, volume: 43, edition: 12, DOI