A time-oscillating Hartree-type Schrödinger equation
Summary: We consider the time-oscillating Hartree-type Schrödinger equation \(i u_t + \Delta u + \theta \left(\omega t\right) \left(\left|x\right|^{- \gamma} * \left|u\right|^2\right) u = 0\), where \(\theta\) is a periodic function. For the mean value \(I(\theta)\) of \(\theta\), we show that the solution \(u_\omega\) converges to the solution of \(i U_t + \Delta U + I \left(\theta\right) \left(\left|x\right|^{- \gamma} * \left|U\right|^2\right) U = 0\) for their local well-posedness and global well-posedness.
scientific article; zbMATH DE number 7023381
scientific article