Zhang, ZihengYuan, Rong2023-06-122023-06-122016-01-27Zhang, Z., & Yuan, R. (2016). Existence of solutions to fractional Hamiltonian systems with combined nonlinearities. Electronic Journal of Differential Equations, 2016(40), pp. 1-13.1072-6691https://hdl.handle.net/10877/16914This article concerns the existence of solutions for the fractional Hamiltonian system -tDα∞(-∞Dtαu(t)) - L(t)u(t) + ∇W(t, u(t)) = 0, u ∈ Hα(ℝ, Rn), where α ∈ (1/2, 1), L ∈ C(ℝ, ℝn2) is a symmetric and positive definite matrix. The novelty of this article is that if τ1|u|2 ≤ (L(t)u, u) ≤ τ2|u|2 and the non-linearity W(t, u) involves a combination of superquadratic and subquadratic terms, the Hamiltonian system possesses at least two nontrivial solutions.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalFractional Hamiltonian systemsCritical pointVariational methodsMountain pass theoremArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.