2014/09/02 by Amado Méndez, Méndez, Amado, César Torres +1 · 1 citation
Mathematics · Physics and Astronomy · #34C37 #35A15 #35B38 #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math-ph #math.MP #msc:34C37 #msc:35A15 #msc:35B38
paper · pdf · doi:10.48550/arxiv.1409.0765
arxiv created 2014/09/02 · openalex publication_date 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the existence of infinitely many solutions for the following fractional Hamiltonian systems: tD∞α(-∞Dtαu(t)) + L(t)u(t) = ∇ W(t,u(t))
u∈ Hα(ℝ, ℝN).where α∈ (1/2, 1), t∈ ℝ, u∈ ℝn, L∈ C(ℝ, ℝn2) is a symmetric and positive definite matrix for all t∈ ℝ, W∈ C1(ℝ× ℝn, ℝ), and ∇ W is the gradient of W at u. The novelty of this paper is that, assuming there exists l∈ C(ℝ, ℝ) such that (L(t)u,u)≥ l(t)|u|2 for all t∈ ℝ, u∈ ℝn and the following conditions on l: inft∈ ℝl(t) >0 and there exists r0>0 such that, for any M>0 m(\t∈ (y-r0, y+r0)/ l(t)≤ M\) → 0 as |y|→ ∞. are satisfied and W is of subquadratic growth as |u| → +∞, we show that (\refeq00) possesses infinitely many solutions via the genus properties in the critical theory. Recent results in [Z. Zhang and R. Yuan, Solutions for subquadratic fractional Hamiltonian systems without coercive conditions, Math. Methods Appl. Sci., DOI: 10.1002/mma.3031] are significantly improved.