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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/2509.11069 |
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| _version_ | 1866915493964677120 |
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| author | Jaure, Diego Maulen, Christopher |
| author_facet | Jaure, Diego Maulen, Christopher |
| contents | We establish existence and uniqueness of remotely almost periodic (RAP) solutions for nonlinear ordinary differential systems $x' = A(t)x + f(t,x) + g_ν(t,x).$ Assuming that the linear equation $x' = A(t)x$ admits an exponential dichotomy and that the associated Green kernel is exponentially bi-remotely almost periodic, we derive sufficient conditions guaranteeing a unique RAP solution of the perturbed system for $ν$ in a suitable range. As an application, we obtain RAP solutions for a nonautonomous Brusselator model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of Remotely Almost Periodic solutions of differential equations and applications Jaure, Diego Maulen, Christopher Dynamical Systems We establish existence and uniqueness of remotely almost periodic (RAP) solutions for nonlinear ordinary differential systems $x' = A(t)x + f(t,x) + g_ν(t,x).$ Assuming that the linear equation $x' = A(t)x$ admits an exponential dichotomy and that the associated Green kernel is exponentially bi-remotely almost periodic, we derive sufficient conditions guaranteeing a unique RAP solution of the perturbed system for $ν$ in a suitable range. As an application, we obtain RAP solutions for a nonautonomous Brusselator model. |
| title | Existence and uniqueness of Remotely Almost Periodic solutions of differential equations and applications |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.11069 |