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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.09250 |
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| _version_ | 1866918139152826368 |
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| author | Tian, Yuzhou Zhang, Meirong |
| author_facet | Tian, Yuzhou Zhang, Meirong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-integrability of the Critical Systems for Optimal Sums of Eigenvalues of Sturm-Liouville Operators Tian, Yuzhou Zhang, Meirong Dynamical Systems 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. |
| title | Non-integrability of the Critical Systems for Optimal Sums of Eigenvalues of Sturm-Liouville Operators |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.09250 |