Characterisation of Convergence, Boundedness and Unboundedness in Solutions of Second Order Linear Differential Equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866912983843602432 |
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| author | Appleby, John A. D. Pal, Subham |
| author_facet | Appleby, John A. D. Pal, Subham |
| contents | This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded, but not convergent, or is unbounded. We see thereby that forcing terms can exhibit unbounded and high--frequency oscillation, and yet the solution may still tend to zero, even though the first and second derivative may become unbounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25545 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterisation of Convergence, Boundedness and Unboundedness in Solutions of Second Order Linear Differential Equations Appleby, John A. D. Pal, Subham Classical Analysis and ODEs This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded, but not convergent, or is unbounded. We see thereby that forcing terms can exhibit unbounded and high--frequency oscillation, and yet the solution may still tend to zero, even though the first and second derivative may become unbounded. |
| title | Characterisation of Convergence, Boundedness and Unboundedness in Solutions of Second Order Linear Differential Equations |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.25545 |