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Hyperbolic-like solutions for singular Hamiltonian systems (2000)

Felmer, Patricio ; Tanaka, Kazunaga

Springer

Nonlinear differential equations and applications 7 (2000), S. 43-65

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ISSN: 1420-9004

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. We study the existence of unbounded solutions of singular Hamiltonian systems: $\ddot q + \nabla V(q) = 0,$ where $V(q) \sim -{1\over{|q|^\alpha}}$ is a potential with a singularity. For a class of singular potentials with a strong force $\alpha〉2$ , we show the existence of at least one hyperbolic-like solutions. More precisely, for given $H〉0$ and $\theta_+, \theta_-\in S^{N-1}$ , we find a solution q(t) of (*) satisfying ${1\over 2} |\dot q|^2 + V(q) = H,$ $|q(t)| \longrightarrow \infty \quad {as} \quad t\longrightarrow\pm\infty$ $\lim \limits_{t\to\pm\infty} {q(t)\over |q(t)|} = \theta_\pm.$

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00001422

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