Electron. J. Differential Equations, Vol. 2020 (2020), No. 29, pp. 1-12.

Existence of solutions to fractional Hamiltonian systems with local superquadratic conditions

Zijun Guo, Qingye Zhang

Abstract:
In this article, we study the existence of solutions for the fractional Hamiltonian system

where $ {}_tD_\infty^\alpha$ and $_{-\infty}D_t^\alpha$ are the Liouville-Weyl fractional derivatives of order $1/2<\alpha<1$, $L\in C(\mathbb{R},\mathbb{R}^{N\times N})$ is a symmetric matrix-valued function, which is unnecessarily required to be coercive, and $W\in C^1(\mathbb{R}\times\mathbb{R}^N,\mathbb{R})$ satisfies some kind of local superquadratic conditions, which is rather weaker than the usual Ambrosetti-Rabinowitz condition.

Submitted September 21, 2019. Published April 6, 2020.
Math Subject Classifications: 26A33, 35A15, 35B38, 37J45.
Key Words: Fractional Hamiltonian system; variational method; superquadratic.
DOI: 10.58997/ejde.2020.29

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Zijun Guo
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang 330022, China
email: 1095752878@qq.com
Qingye Zhang
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang 330022, China
email: qingyezhang@gmail.com

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