Existence of solutions to fractional Hamiltonian systems with local superquadratic conditions

Date

2020-04-06

Authors

Guo, Zijun
Zhang, Qingye

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Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we study the existence of solutions for the fractional Hamiltonian system tDα∞ (-∞Dαtu(t)) + L(t)u(t) = ∇W(t, u(t)), u ∈ Hα (ℝ, ℝN), where tDα∞ and -∞Dαt are the Liouville-Weyl fractional derivatives of order 1/2 < α < 1, L ∈ C (ℝ, ℝNxN) is a symmetric matrix-valued function, which is unnecessarily required to be coercive, and W ∈ C1 (ℝ x ℝN, ℝ) satisfies some kind of local superquadratic conditions, which is rather weaker than the usual Ambrosetti-Rabinowitz condition.

Description

Keywords

Fractional Hamiltonian system, Variational method, Superquadratic

Citation

Guo, Z., & Zhang, Q. (2020). Existence of solutions to fractional Hamiltonian systems with local superquadratic conditions. <i>Electronic Journal of Differential Equations, 2020</i>(29), pp. 1-12.

Rights

Attribution 4.0 International

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