Homoclinic solutions for second-order non-autonomous Hamiltonian systems without global Ambrosetti-Rabinowitz conditions

This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system $$ ddot q-L(t)q+W_{q}(t,q)=0, $$ where $Lin C(mathbb{R},mathbb{R}^{n^2})$ is a symmetric and positive definite matrix for all $tin mathbb{R}$. The function $Win C^{1}(mathbb{R}ime...

Full description

Bibliographic Details
Published in:Electronic Journal of Differential Equations
Main Authors: Rong Yuan, Ziheng Zhang
Format: Article
Language:English
Published: Texas State University 2010-02-01
Subjects:
Homoclinic solutions
critical point
variational methods
mountain pass theorem
Online Access:http://ejde.math.txstate.edu/Volumes/2010/29/abstr.html
Description
Summary:This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system $$ ddot q-L(t)q+W_{q}(t,q)=0, $$ where $Lin C(mathbb{R},mathbb{R}^{n^2})$ is a symmetric and positive definite matrix for all $tin mathbb{R}$. The function $Win C^{1}(mathbb{R}imesmathbb{R}^{n},mathbb{R})$ is not assumed to satisfy the global Ambrosetti-Rabinowitz condition. Assuming reasonable conditions on $L$ and $W$, we prove the existence of at least one nontrivial homoclinic solution, and for $W(t,q)$ even in $q$, we prove the existence of infinitely many homoclinic solutions.
ISSN:1072-6691

Similar Items