TY - JOUR

T1 - Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ, 1 with β = max (frac(3, 2), 1 + frac(2, n)) for the nonlinear Klein-Gordon equation with a power nonlinearityut t - Δ u + u = μ | u |σ - 1 u, (t, x) ∈ R × Rn, where 1 + frac(4, n + 2) < σ < 1 + frac(4, n) for n ≥ 3, μ ∈ C.

AB - We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ, 1 with β = max (frac(3, 2), 1 + frac(2, n)) for the nonlinear Klein-Gordon equation with a power nonlinearityut t - Δ u + u = μ | u |σ - 1 u, (t, x) ∈ R × Rn, where 1 + frac(4, n + 2) < σ < 1 + frac(4, n) for n ≥ 3, μ ∈ C.

KW - Asymptotics of solutions

KW - Higher space dimensions

KW - Nonlinear Klein-Gordon equations

KW - Power nonlinearities

KW - Scattering operator

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U2 - 10.1016/j.jde.2007.10.002

DO - 10.1016/j.jde.2007.10.002

M3 - Article

AN - SCOPUS:36048947313

SN - 0022-0396

VL - 244

SP - 188

EP - 199

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -