Multiplicity of solutions for nonperiodic perturbed fractional Hamiltonian systems
Date
2017-03-30
Authors
Benhassine, Abderrazek
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Fractional Hamiltonian systems, Critical point, Variational methods
Citation
Benhassine, A. (2017). Multiplicity of solutions for nonperiodic perturbed fractional Hamiltonian systems. <i>Electronic Journal of Differential Equations, 2017</i>(93), pp. 1-15.
Rights
Attribution 4.0 International