Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities
This article concerns the existence of fast homoclinic solutions for the following damped vibration system\begin{equation*}\frac{d}{dt}(P(t)\dot{u}(t))+q(t)P(t)\dot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0,\end{equation*}where $P,L\in C\left(\mathbb{R},\mathbb{R}^{N^{2}}\right)$ are symmetric and positive...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2024-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_708349_4bdf4975098814b54809b27a9a5c9dcc.pdf |
| _version_ | 1797359753354018816 |
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| author | Mohsen Timoumi |
| author_facet | Mohsen Timoumi |
| author_sort | Mohsen Timoumi |
| collection | DOAJ |
| description | This article concerns the existence of fast homoclinic solutions for the following damped vibration system\begin{equation*}\frac{d}{dt}(P(t)\dot{u}(t))+q(t)P(t)\dot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0,\end{equation*}where $P,L\in C\left(\mathbb{R},\mathbb{R}^{N^{2}}\right)$ are symmetric and positive definite matrices, $q\in C\left(\mathbb{R},\mathbb{R}\right)$ and $W\in C^{1}\left(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R}\right)$. Applying the Fountain Theorem and Dual Fountain Theorem, we prove the above system possesses two different sequences of fast homoclinic solutions when $L$ satisfies a new coercive condition and the potential $W(t,x)$ is combined nonlinearity. |
| first_indexed | 2024-03-08T15:29:17Z |
| format | Article |
| id | doaj.art-3fc806a9317c4d90858b8ad7070ba110 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-03-08T15:29:17Z |
| publishDate | 2024-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-3fc806a9317c4d90858b8ad7070ba1102024-01-10T07:27:09ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-01-0121123725410.22130/scma.2023.1975918.1211708349Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined NonlinearitiesMohsen Timoumi0Department of Mathematics, Faculty of Sciences, University of Monastir, P.O.Box 5019, Monastir, Tunisia.This article concerns the existence of fast homoclinic solutions for the following damped vibration system\begin{equation*}\frac{d}{dt}(P(t)\dot{u}(t))+q(t)P(t)\dot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0,\end{equation*}where $P,L\in C\left(\mathbb{R},\mathbb{R}^{N^{2}}\right)$ are symmetric and positive definite matrices, $q\in C\left(\mathbb{R},\mathbb{R}\right)$ and $W\in C^{1}\left(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R}\right)$. Applying the Fountain Theorem and Dual Fountain Theorem, we prove the above system possesses two different sequences of fast homoclinic solutions when $L$ satisfies a new coercive condition and the potential $W(t,x)$ is combined nonlinearity.https://scma.maragheh.ac.ir/article_708349_4bdf4975098814b54809b27a9a5c9dcc.pdfdamped vibration systemsfast homoclinic solutionsvariational methodsfountain theoremdual fountain theorem |
| spellingShingle | Mohsen Timoumi Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities Sahand Communications in Mathematical Analysis damped vibration systems fast homoclinic solutions variational methods fountain theorem dual fountain theorem |
| title | Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities |
| title_full | Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities |
| title_fullStr | Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities |
| title_full_unstemmed | Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities |
| title_short | Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities |
| title_sort | infinitely many fast homoclinic solutions for damped vibration systems with combined nonlinearities |
| topic | damped vibration systems fast homoclinic solutions variational methods fountain theorem dual fountain theorem |
| url | https://scma.maragheh.ac.ir/article_708349_4bdf4975098814b54809b27a9a5c9dcc.pdf |
| work_keys_str_mv | AT mohsentimoumi infinitelymanyfasthomoclinicsolutionsfordampedvibrationsystemswithcombinednonlinearities |