Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.09250 |
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Inhaltsangabe:
- The optimal lower or upper bounds for sums of the first $m$ eigenvalues of Sturm-Liouville operators can be obtained by solving the corresponding critical systems, which are Hamiltonian systems of $m$ degrees of freedom with $m$ parameters. With the help of the differential Galois theory, we prove that these critical systems are not meromorphic integrable except for two known completely integrable cases. The non-integrability of the critical systems reveal certain complexities for the original eigenvalues problems.