A 2D Schrodinger equation with time-oscillating exponential nonlinearity

This paper deals with the 2-D Schr"odinger equation with time-oscillating exponential nonlinearity $i\partial_t u+\Delta u= \theta(\omega t)\big(e^{4\pi|u|^2}-1\big)$,where$\theta$isaperiodic$C^1$-function. We prove that for a class of initial data $u_0\in H^1({\mathbb{R}}^2)$, the solution $u_{\omega }$ converges, as $\mathrm{\mid }\omega \mathrm{\mid }$ tends to infinity to the solution $U$ of the limiting equation $i\partial_t U+\Delta U= I(\theta)\big(e^{4\pi|U|^2}-1\big)$withthesameinitialdata,where$I(\theta)$istheaverageof$\theta$.