Benhassine, Abderrazek2022-04-082022-04-082017-03-30Benhassine, A. (2017). Multiplicity of solutions for nonperiodic perturbed fractional Hamiltonian systems. <i>Electronic Journal of Differential Equations, 2017</i>(93), pp. 1-15.1072-6691https://hdl.handle.net/10877/15625In this article, we prove the existence and multiplicity of nontrivial solutions for the nonperiodic perturbed fractional Hamiltonian systems -tDα∞(-∞Dαtx(t)) - λL(t) · x(t) + ∇W(t, x(t)) = ƒ(t), x ∈ Hα (ℝ, ℝN), where α ∈ (1/2, 1], λ > 0 is a parameter, t ∈ ℝ, x ∈ ℝN, -∞Dαt and tDα∞ are left and right Liouville-Weyl fractional derivatives of order α on the whole axis ℝ respectively, the matrix L(t) is not necessary positive definite for all t ∈ ℝ nor coercive, W ∈ C1 (ℝxℝN) and ƒ ∈ L2(ℝ, ℝN)\{0} small enough. Replacing the Ambrosetti-Rabinowitz Condition by general superquadratic assumptions, we establish the existence and multiplicity results for the above system. Some examples are also given to illustrate our results.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalFractional Hamiltonian systemsCritical pointVariational methodsArticle