Mohsen Timoumi, Existence and multiplicity of solutions for a class of fractional Hamiltonian systems with separated variables, Vol. 2023 (2023), Article ID 25, pp. 1-17

Full Text: PDF
DOI: 10.23952/jnfa.2023.25

Received April 15, 2023; Accepted July 12, 2023; Published August 7, 2023

Abstract. In this paper, we study the existence and multiplicity of solutions of a class of fractional Hamiltonian systems with variable separated type nonlinear terms
$_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u)(t)+L(t)u(t)=a(t)\nabla G(u(t)),$ $t\in\mathbb{R},$
$u\in H^{\alpha}(\mathbb{R}),$
where $L$ satisfies a new condition and the potential $G$ satisfies a superquadratic condition weaker than the well-known Ambrosetti-Rabinowitz condition. Moreover, under a new mixed condition, we establish a compact embedding theorem.

How to Cite this Article:
M. Timoumi, Existence and multiplicity of solutions for a class of fractional Hamiltonian systems with separated variables, J. Nonlinear Funct. Anal. 2023 (2023) 25.