Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part

2024/05/31 by Federico Bernini, Bernini, Federico, Bartosz Bieganowski +3
Computer Science · Mathematics · #35A15 #37C29 #37J46 #58E05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2405.20908

openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system z = J D_z H(z, t), t ∈ ℝ, where the Hamiltonian H : ℝ^2N × ℝ → ℝ is of the form H(z, t) = \frac12 Az ⋅ z + Γ(t) ( F(z) - λG(z) ) for some symmetric matrix A.

Related

• Global bifurcation of homoclinic solutions of hamiltonian systems
• Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems
• Existence of homoclinic solution in first order discrete Hamiltonian system
• New homoclinic orbits for Hamiltonian systems with asymptotically quadratic growth at infinity
• Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems