Academic Journal
Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations
| العنوان: | Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations |
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| المؤلفون: | Carletti, Timoteo, Villari, Gabriele, Zanolin, Fabio |
| المصدر: | Carletti , T , Villari , G & Zanolin , F 2022 , ' Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations ' , Monatshefte für Mathematik , vol. 199 , no. 2 , pp. 243-257 . https://doi.org/10.1007/s00605-021-01652-3 |
| سنة النشر: | 2022 |
| المجموعة: | Research Portal - University of Namur / Portail de la recherche de l'Université de Namur |
| مصطلحات موضوعية: | non-autonomous systems, generalised Liénard equation, prescribed curvature operator, relativistic acceleration, p-Laplacian, positively invariant sets, Brouwer fixed point, periodic orbits, Generalized Liénard equations, φ-Laplacian, Brouwer fixed point theorem |
| الوصف: | We study the problem of existence of harmonic solutions for some generalisations of the periodically perturbed Liénard equation, where the damping function depends both on the position and the velocity. In the associated phase-space this corresponds to a term of the form f(x, y) instead of the standard dependence on x alone. We introduce suitable autonomous systems to control the orbits behaviour, allowing thus to construct invariant regions in the extended phase-space and to conclude about the existence of the harmonic solution, by invoking the Brouwer fixed point Theorem applied to the Poincaré map. Applications are given to the case of the p-Laplacian and the prescribed curvature equation. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| DOI: | 10.1007/s00605-021-01652-3 |
| الاتاحة: | https://researchportal.unamur.be/en/publications/7fbdd4d1-3b58-4fcd-9619-40b6c4646bb9 https://doi.org/10.1007/s00605-021-01652-3 https://pure.unamur.be/ws/files/62313822/CarlettiVillariZanolinNonAuto_1.pdf http://www.scopus.com/inward/record.url?scp=85122695077&partnerID=8YFLogxK https://link.springer.com/article/10.1007%2Fs00605-021-01652-3#citeas |
| Rights: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.54F397D2 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/s00605-021-01652-3 |
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