Renormalized oscillation theory for linear Hamiltonian systems on \([0, 1]\) via the Maslov index. (English) Zbl 07818470
Summary: Working with a general class of regular linear Hamiltonian systems, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated with appropriately chosen paths of Lagrangian subspaces of \(\mathbb{C}^{2n}\). We verify that our applicability class includes Dirac and Sturm-Liouville systems, as well as a system arising from differential-algebraic equations for which the spectral parameter appears nonlinearly.
MSC:
| 37J51 | Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods |
| 53D12 | Lagrangian submanifolds; Maslov index |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
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