抄録
We consider the scattering problem for the Hartree type equation in ℝn with n≧2: {Mathematical expression} where {Mathematical expression} and * denotes the convolution in ℝn. We prove the existence of wave operators in H0, k = {ψ∈L2(ℝn);|x|kψ∈L2(ℝn)} for any positive integer k under the assumption 1<γ1, γ2<2. This is an optimal result in the sense that the existence of wave operators breaks down if min (γ1, γ2≢1. The case where 1<γ1, γ2 = 2 is also treated according to the sign of λ2.
本文言語 | English |
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ページ(範囲) | 259-275 |
ページ数 | 17 |
ジャーナル | Communications in Mathematical Physics |
巻 | 146 |
号 | 2 |
DOI | |
出版ステータス | Published - 1992 5 1 |
外部発表 | はい |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics