Characterization of Maximizers for Sums of the First Two Eigenvalues of Sturm-Liouville Operators
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915839217762304 |
|---|---|
| author | Meng, Gang Tian, Yuzhou Xie, Bing Zhang, Meirong |
| author_facet | Meng, Gang Tian, Yuzhou Xie, Bing Zhang, Meirong |
| contents | In this paper we study the maximization of the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators with potentials in the noncompact space $L^1$. We prove that there exists a unique potential function achieving the maximum, which is non-negative, piecewise smooth, and symmetric. Using measure differential equations and weak$^*$ convergence, we show that the nonzero part of the maximizer can be determined by the solution to the pendulum equation $θ'' + \ell \sinθ= 0 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of Maximizers for Sums of the First Two Eigenvalues of Sturm-Liouville Operators Meng, Gang Tian, Yuzhou Xie, Bing Zhang, Meirong Dynamical Systems In this paper we study the maximization of the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators with potentials in the noncompact space $L^1$. We prove that there exists a unique potential function achieving the maximum, which is non-negative, piecewise smooth, and symmetric. Using measure differential equations and weak$^*$ convergence, we show that the nonzero part of the maximizer can be determined by the solution to the pendulum equation $θ'' + \ell \sinθ= 0 $. |
| title | Characterization of Maximizers for Sums of the First Two Eigenvalues of Sturm-Liouville Operators |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.06019 |