Even homoclinic orbits for a non periodic dynamical systems

  • Fathi Khelifi mathe'matiques
  • Mohsen Timoumi

Abstract

In this paper, we study the existence of even homoclinic solutions
for a nonperiodic dynamical system
$$ \ddot{x}(t)+A\dot{x}(t)+V'(t,x(t))=0,$$ where A is a skew-symmetric constant matrix, t $\in\mathbb{R}$, $x\in\mathbb{R}^N$ and V $\in C^1(\mathbb{R}\times\mathbb{R}^N,\mathbb{R})$,
$V(t,x)=-K(t,x)+W(t,x)$. We assume that $W(t,x)$ does not satisfy the global Ambrosetti-Rabinowitz condition and that the norm of A is sufficiently small.

Published
Nov 26, 2017
How to Cite
KHELIFI, Fathi; TIMOUMI, Mohsen. Even homoclinic orbits for a non periodic dynamical systems. Nonlinear Studies, [S.l.], v. 24, n. 4, p. 921-933, nov. 2017. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/1580>. Date accessed: 15 dec. 2017.