2015/03/23 by César E. Torres Ledesma, Ledesma, César E. Torres
Mathematics · Physics and Astronomy · #26A33 #34C37 #35A15 #35B38 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:26A33 #msc:34C37 #msc:35A15 #msc:35B38
paper · pdf · doi:10.48550/arxiv.1503.06829
arXiv admin note: text overlap with arXiv:1409.0765
arxiv created 2015/03/23 · openalex publication_date 2015/03/23 · arxiv updated 2015/03/25 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
This article study the fractional Hamiltonian systems tD∞α(-∞Dtαu) + λL(t)u = ∇ W(t, u), t∈ ℝ, where α∈ (1/2, 1), λ>0 is a parameter, L∈ C(ℝ, ℝn× n) and W ∈ C1(ℝ × ℝn, ℝ). Unlike most other papers on this problem, we require that L(t) is a positive semi-definite symmetric matrix for all t∈ ℝ, that is, L(t) ≡ 0 is allowed to occur in some finite interval \mathbbI of ℝ. Under some mild assumptions on W, we establish the existence of nontrivial weak solution, which vanish on ℝ ∖ \mathbbI as λ→ ∞, and converge to u in Hα(ℝ); here u ∈ E0α is nontrivial weak solution of the Dirichlet BVP for fractional Hamiltonian systems on the finite interval \mathbbI.