International Journal of Nonlinear Analysis and Applications

Ground state solutions for two classes of fractional Hamiltonian systems

Articles in Press

Document Type : Research Paper

Author

Dpt of Mathematics, Faculty of Sciences of Monastir, 5000 Monastir, Tunisia

Abstract

In this paper, we are concerned with the following periodic fractional Hamiltonian system
$$\left\{
\begin{array}{l}
_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u)(t)+L(t)u(t)=\nabla W(t,u(t)),\ t\in\mathbb{R}\\
u\in H^{\alpha}(\mathbb{R}).
\end{array}\right.$$
Using variational methods and a version of the concentration compactness principle, we study the existence of ground state solutions for this system under two different classes of superquadratic conditions weaker than the ones known in the literature. To the best of our knowledge, there has been no work focused in this case.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 15 April 2026
  • Receive Date: 06 August 2022
  • Revise Date: 12 June 2023
  • Accept Date: 15 February 2025