Existence of weak quasi-periodic solutions for a second order Hamiltonian system with damped term via a PDE approach

• Published in: Electronic journal of qualitative theory of differential equations Vol. 2016; no. 109; pp. 1 - 14
• Main Authors: Zhang, Xingyong, Wang, Liben
• Format: Journal Article
• Language: English
• Published: University of Szeged 01.01.2016
• Subjects: damped term; pde approach; second order hamiltonian system; variational method; weak quasi-periodic solution
• ISSN: 1417-3875; 1417-3875
• DOI: 10.14232/ejqtde.2016.1.109

In this paper, we investigate the existence of weak quasi-periodic solutions for the second order Hamiltonian system with damped term: \begin{equation} \ddot{u}(t)+q(t)\dot{u}(t)+D W(u(t))=0, \qquad t\in \mathbb R,\tag{HSD} \end{equation} where $u:\mathbb R\to \mathbb R^n$, $q:\mathbb R\to \mathbb R...