Characterisation of Stability and Decay Rates in a Weakly Damped Second Order Linear Differential Equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912983849893888 |
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| author | Appleby, John A. D. Pal, Subham |
| author_facet | Appleby, John A. D. Pal, Subham |
| contents | This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are asymptotically stable. Conditions are also given which characterise when the solution and its derivative tend to zero. Finally, we give sharp sufficient conditions under which the solution of the forced equation has the same asymptotic behaviour as the unforced equation, to leading order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25547 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterisation of Stability and Decay Rates in a Weakly Damped Second Order Linear Differential Equation Appleby, John A. D. Pal, Subham Classical Analysis and ODEs This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are asymptotically stable. Conditions are also given which characterise when the solution and its derivative tend to zero. Finally, we give sharp sufficient conditions under which the solution of the forced equation has the same asymptotic behaviour as the unforced equation, to leading order. |
| title | Characterisation of Stability and Decay Rates in a Weakly Damped Second Order Linear Differential Equation |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.25547 |