Continuation theorems for periodic systems and applications to problems with nonlinear time-dependent differential operators
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911338883710976 |
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| author | Benevieri, Pierluigi Feltrin, Guglielmo |
| author_facet | Benevieri, Pierluigi Feltrin, Guglielmo |
| contents | In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1},\ldots,x_{n}), \\ \, x_{i}(0)=x_{i}(T), &i=1,\ldots,n, \end{cases} \end{equation*} providing a unified framework that improves and extends earlier contributions by Jean Mawhin and collaborators to second-order differential problems governed by nonlinear time-dependent differential operators of the form \begin{equation*} \begin{cases} \, (ϕ(t,x'))'=f(t,x,x'), \\ \, x(0)=x(T),\quad x'(0)=x'(T). \end{cases} \end{equation*} The proof is based on the topological degree theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuation theorems for periodic systems and applications to problems with nonlinear time-dependent differential operators Benevieri, Pierluigi Feltrin, Guglielmo Classical Analysis and ODEs 34B15, 34C25, 47H11, 47J05 In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1},\ldots,x_{n}), \\ \, x_{i}(0)=x_{i}(T), &i=1,\ldots,n, \end{cases} \end{equation*} providing a unified framework that improves and extends earlier contributions by Jean Mawhin and collaborators to second-order differential problems governed by nonlinear time-dependent differential operators of the form \begin{equation*} \begin{cases} \, (ϕ(t,x'))'=f(t,x,x'), \\ \, x(0)=x(T),\quad x'(0)=x'(T). \end{cases} \end{equation*} The proof is based on the topological degree theory. |
| title | Continuation theorems for periodic systems and applications to problems with nonlinear time-dependent differential operators |
| topic | Classical Analysis and ODEs 34B15, 34C25, 47H11, 47J05 |
| url | https://arxiv.org/abs/2512.21554 |