## Long range scattering and modified wave operators for some Hartree type equations. II.(English)Zbl 1024.35084

The authors study the scattering theory for a class of Hartree type equations with long range interactions in space dimension $$n \geq 3$$, including Hartree equations with potential $$V(x)=\lambda |x|^{-\gamma}, 0 < \gamma \leq 1$$. They prove the existence of modified wave operators. The asymptotic behaviour in time of solutions in the range of the wave operators is also investigated.
For Part I, cf. Rev. Math. Phys. 12, 361-429 (2000; Zbl 1044.35041).

### MSC:

 35P25 Scattering theory for PDEs 81U99 Quantum scattering theory 35B40 Asymptotic behavior of solutions to PDEs 35Q40 PDEs in connection with quantum mechanics

### Keywords:

existence; asymptotic behaviour

Zbl 1044.35041
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