@Article{CMR-41-148,
author = {Zhu , WenzhuangHu , Chunhui and Ji , Shuguan},
title = {Homoclinic Solutions for a Class of Hamiltonian Systems with Small External Perturbations},
journal = {Communications in Mathematical Research },
year = {2025},
volume = {41},
number = {2},
pages = {148--172},
abstract = {<p style="text-align: justify;">This paper is concerned with the existence of nontrivial homoclinic
solutions for a class of second order Hamiltonian systems with external forcing perturbations $\ddot{q}+A\dot{q}+V_q(t,q)= f(t),$ where $q= (q_1,q_2,···,q_N)∈\mathbb{R}^N,$ $A$ is an
antisymmetric constant $N×N$ matrix, $V(t,q) = −K(t,q)+W(t,q)$ with $K,W ∈
C^1
(\mathbb{R},\mathbb{R}^N)$ and satisfying $b_1|q|^2 ≤ K(t,q) ≤ b_2|q|^2$ for some positive constants $b_2 ≥b_1 &gt;0$ and external forcing term $f ∈C(\mathbb{R},\mathbb{R}^N)$ being small enough. Under
some new weak superquadratic conditions for $W,$ by using the mountain pass
theorem, we obtain the existence of at least one nontrivial homoclinic solution.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2025-0016},
url = {http://global-sci.org/intro/article_detail/cmr/24189.html}
}