#### Mohsen Timoumi, Infinitely many fast homoclinic solutions for different classes of damped vibration systems, Vol. 2020 (2020), Article ID 46, pp. 1-20

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DOI: 10.23952/jnfa.2020.46

Received September 19, 2020; Accepted October 22, 2020; Published November 7, 2020

Abstract. In this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems $\ddot{u}(t)+(q(t)I_{N}+B)\dot{u}(t)+\frac{1}{2}q(t)Bu(t)-L(t)u(t)+\nabla W(t,u(t))=0,$ $\forall t\in\mathbb{R},$ where $L(t)$ is not required to be either uniformly positive definite or coercive, and $W(t,x)$ is of subquadratic or superquadratic growth as $\left|x\right|\rightarrow\infty$, or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at infinity). To the best of our knowledge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.

How to Cite this Article:
Mohsen Timoumi, Infinitely many fast homoclinic solutions for different classes of damped vibration systems, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 46, pp. 1-20.