@article {
author = {Timoumi, Mohsen},
title = {Infinitely Many Fast Homoclinic Solutions for Damped Vibration Systems with Combined Nonlinearities},
journal = {Sahand Communications in Mathematical Analysis},
volume = {21},
number = {1},
pages = {237-254},
year = {2024},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.1975918.1211},
abstract = {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.},
keywords = {Damped vibration systems,Fast homoclinic solutions,Variational methods,Fountain Theorem,Dual Fountain Theorem},
url = {https://scma.maragheh.ac.ir/article_708349.html},
eprint = {https://scma.maragheh.ac.ir/article_708349_4bdf4975098814b54809b27a9a5c9dcc.pdf}
}