Existence of solution for perturbed fractional Hamiltonian systems

2014/02/27 by César Torres, Torres, César
Mathematics · #Analysis of PDEs (math.AP) #Combinatorics #Differential Equations and Numerical Methods #FOS: Mathematics #Hamiltonian (control theory) #Infinity #Mathematical analysis #Mathematical physics #Mathematics #Nabla symbol #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Omega #Physics #Quantum mechanics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.6919

arXiv admin note: substantial text overlap with arXiv:1212.5811

arxiv created 2014/02/27 · openalex publication_date 2014/02/27 · arxiv updated 2014/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we prove the existence of solution for a class of perturbed fractional Hamiltonian systems given by -_tD_∞^α(_-∞D_t^αu(t)) - L(t)u(t) + ∇ W(t,u(t)) = f(t), where α∈ (1/2, 1), t∈ ℝ, u∈ ℝⁿ, L∈ C(ℝ, ℝ^n²) 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 L is coercive at infinity we show that (\refeq00) at least has one nontrivial solution.

Citations

• Fractional Differential Equations
• Existence of solution for a class of fractional Hamiltonian systems

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