@article{Janczewska_2010, title={Homoclinic solutions for a class of autonomous second order Hamiltonian systems with a superquadratic potential}, volume={36}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2010.025}, abstractNote={We will prove the existence of a nontrivial homoclinic solution
for an autonomous second order Hamiltonian system
$\ddot{q}+
abla{V}(q)=0$, where $q\in\mathbb{R}^n$, a potential
$V\colon\mathbb{R}^n\to\mathbb{R}$ is of the form $V(q)=-K(q)+W(q)$, $K$ and $W$ are $C^{1}$-maps, $K$ satisfies the pinching
condition, $W$ grows at a superquadratic rate, as $|q|\to\infty$ and $W(q)=o(|q|^2)$, as $|q|\to 0$. A homoclinic solution will be obtained as a weak limit
in the Sobolev space $W^{1,2}(\mathbb{R},\mathbb{R}^n)$ of a sequence
of almost critical points of the corresponding action functional. Before passing to a weak limit with a sequence of
almost critical points each element of this sequence has to be
appropriately shifted.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Janczewska, Joanna}, year={2010}, month={Apr.}, pages={19–26} }