Hyperbolic-like solutions for singular Hamiltonian systems

Patricio Felmer, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We study the existence of unbounded solutions of singular Hamiltonian systems: q̈ + ∇V(q)=0, (*) where V(q) ∼ -1/|q|α is a potential with a singularity. For a class of singular potentials with a strong force α > 2, we show the existence of at least one hyperbolic-like solutions. More precisely, for given H > 0 and θ+, θ- ε SN-1, we find a solution q(t) of (*) satisfying 1/2 |q̇|2 + V(q) = H, |q(t) |→ as t → ±∞ limt→±∞ q(t)/|q(t)|=θ±.

    Original languageEnglish
    Pages (from-to)43-65
    Number of pages23
    JournalNonlinear Differential Equations and Applications
    Volume7
    Issue number1
    Publication statusPublished - 2000

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    Hamiltonians
    Singular Systems
    Hamiltonian Systems
    Unbounded Solutions
    Singular Potential
    Singularity
    Class

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Hyperbolic-like solutions for singular Hamiltonian systems. / Felmer, Patricio; Tanaka, Kazunaga.

    In: Nonlinear Differential Equations and Applications, Vol. 7, No. 1, 2000, p. 43-65.

    Research output: Contribution to journalArticle

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    AB - We study the existence of unbounded solutions of singular Hamiltonian systems: q̈ + ∇V(q)=0, (*) where V(q) ∼ -1/|q|α is a potential with a singularity. For a class of singular potentials with a strong force α > 2, we show the existence of at least one hyperbolic-like solutions. More precisely, for given H > 0 and θ+, θ- ε SN-1, we find a solution q(t) of (*) satisfying 1/2 |q̇|2 + V(q) = H, |q(t) |→ as t → ±∞ limt→±∞ q(t)/|q(t)|=θ±.

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