Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems

Xiaoyan Lin, Qi-Ming Zhang and X. H. Tang

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We give several sufficient conditions under which the first‐order nonlinear Hamiltonian system x′(t) = α(t)x(t) + f(t, y(t)), y′(t) = −g(t, x(t)) − α(t)y(t) has no solution (x(t), y(t)) satisfying condition 0 1 and (1/μ) + (1/ν) = 1, 0 ≤ xf(t, x) ≤ β(t) | x|μ, xg(t, x) ≤ γ0(t) | x|ν, β(t), γ0(t) ≥ 0, and α(t) are locally Lebesgue integrable real‐valued functions defined on ℝ.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:547682

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