Electron. J. Differential Equations, Vol. 2019 (2019), No. 43, pp. 1-17.

Fast homoclinic solutions for damped vibration systems with subquadratic and asymptotically quadratic potentials

Yiwei Ye

Abstract:
In this article, we study the nonperiodic damped vibration problem
$$ \ddot{u}(t)+q(t)\dot u(t)-L(t)u(t)+\nabla W(t,u(t))=0, $$
where L(t) is uniformly positive definite for all $t\in \mathbb{R}$, and W(t,x) is either subquadratic or asymptotically quadratic in x as $|x|\to \infty$. Based on the minimax method in critical point theory, we prove the existence and multiplicity of fast homoclinic solutions for the above problem.

Submitted November 3, 2017. Published March 22, 2019.
Math Subject Classifications: 34C37, 37J45.
Key Words: Fast homoclinic solutions; damped vibration problem; subquadratic; asymptotically quadratic.

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Yiwei Ye
School of Mathematical Science
Chongqing Normal University
Chongqing 401331, China
email: yeyiwei2011@126.com

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