Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 43, pp. 1-17.

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

Author: Yiwei Ye (Chongqing Normal Univ., Chongqing, China)
 
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.