A Time-Oscillating Hartree-Type Schrödinger Equation

Abstract EN

We consider the time-oscillating Hartree-type Schrödinger equation i u t + Δ u + θ ω t x - γ * u 2 u = 0 , where θ is a periodic function.

For the mean value I ( θ ) of θ , we show that the solution u ω converges to the solution of i U t + Δ U + I θ x - γ * U 2 U = 0 for their local well-posedness and global well-posedness.