Existence and multiplicity of solutions for a class of Hamiltonian systems
UDC 517.9 We investigate a class of Hamiltonian systems \begin{gather*} {-q''}(t)+(L(t)-\xi)q(t)= a(t)|q(t)|^{p-2}q(t)+\eta f(t),\\ q\in H^1(\mathbb{R},\mathbb{R}^N),\end{gather*} where $(t,q)\in \mathbb{R}\times \mathbb{R}^N$, $p>2,$ $a\in C(\mathbb{R},(0,+\infty)),$ $f...
Збережено в:
| Дата: | 2024 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7497 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.9
We investigate a class of Hamiltonian systems \begin{gather*} {-q''}(t)+(L(t)-\xi)q(t)= a(t)|q(t)|^{p-2}q(t)+\eta f(t),\\ q\in H^1(\mathbb{R},\mathbb{R}^N),\end{gather*} where $(t,q)\in \mathbb{R}\times \mathbb{R}^N$, $p>2,$ $a\in C(\mathbb{R},(0,+\infty)),$ $f\in C(\mathbb{R},\mathbb{R}^N),$ $\xi, \eta$ are real parameters, and $L\in C(\mathbb{R},\mathbb{R}^{N^2})$ is a positive definite symmetric matrix for all $t\in \mathbb{R}.$ The main technical approach is based on the Nehari manifold method combined with variational and topological methods. The obtained results extend and complement the results available in the literature. |
|---|---|
| DOI: | 10.3842/umzh.v76i5.7497 |