Scattering for the Radial Schrödinger Equation with Combined Power-type and Choquard-type Nonlinearities.

In this paper, we show the scattering of the radial solution for the nonlinear Schrödinger equation with combined power-type and Choquard-type nonlinearities i u t + Δ u = λ 1 ∣ u ∣ p 1 − 1 u + λ 2 (I α ∗ ∣ u ∣ p 2 ) ∣ u ∣ p 2 − 2 u. in the energy space H1(ℝN) for λ1λ2 = −1. We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory. Results show that the defocusing perturbation terms does not determine the scattering solution in energy space. [ABSTRACT FROM AUTHOR]