Existence and multiplicity of solutions for a class of Hamiltonian systems

Khaled Khachnaoui

doi:10.3842/umzh.v76i5.7497

Khaled Khachnaoui Department of Mathematics, University of Kairouan, Preparatory Institute for Engineering Studies, Tunisia

DOI: https://doi.org/10.3842/umzh.v76i5.7497

Анотація

УДК 517.9

Існування та множинність розв’язків для одного класу гамільтонових систем

Mи досліджуємо клас гамільтонoвих систем \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} де $(t,q)\in \mathbb{R}\times \mathbb{R}^N$, $p>2,$ $a\in C(\mathbb{R},(0,+\infty)),$ $f\in C(\mathbb{R},\mathbb{R}^N),$ $\xi$ та $\eta$ --- дійсні параметри і $L\in C(\mathbb{R},\mathbb{R}^{N^2})$ — додатно визначена симетрична матриця для всіх $t\in \mathbb{R}.$ Основний технічний підхід базується на методі многовиду Нехарі спільно з варіаційними і топологічними методами. Отримані результати розширюють і доповнюють результати, доступні в літературі.

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