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November/December 2015 Scattering operator for semirelativistic Hartree type equation with a short range potential
Nakao Hayashi, Pavel I. Naumkin, Takayoshi Ogawa
Differential Integral Equations 28(11/12): 1085-1104 (November/December 2015).

Abstract

We prove the existence of the scattering operator in the neighborhood of the origin in $\mathbf{H}^{\omega ,1}\cap \mathbf{H}^{\mu },$ where $\mu > \omega =1+\frac{2}{n}$ for the semirelativistic Hartree type equation \begin{equation*} i\partial _{t}u=\sqrt{M^{2}-\Delta }u+F \big ( u \big ) ,\text{ } \big ( t,x \big ) \in {\mathbf{R}}\times {\mathbf{R}}^{n}, \end{equation*} where $F ( u ) = ( | x | ^{-\gamma }\ast | u | ^{2} ) u,1 < \gamma < 2,n\geq 3$ and $\ast $ denotes the convolution.

Citation

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Nakao Hayashi. Pavel I. Naumkin. Takayoshi Ogawa. "Scattering operator for semirelativistic Hartree type equation with a short range potential." Differential Integral Equations 28 (11/12) 1085 - 1104, November/December 2015.

Information

Published: November/December 2015
First available in Project Euclid: 18 August 2015

zbMATH: 1374.35330
MathSciNet: MR3385136

Subjects:
Primary: 35Q40, 35Q55, 47J35

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 11/12 • November/December 2015
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