Existence and multiplicity of solutions for a class of Hamiltonian systems

• Date: 2024
• Main Author: Khachnaoui, Khaled
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7497
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...