Convergence of a class of Schrödinger equations

Abstract

We set up the selection conditions for time series ${\left\{t_k\right\}}_{k=1}^{\infty }$ which converge to 0 as $k\to \infty$ and for which the solutions of a class of generalized Schrödinger equations pointwise converge almost everywhere to their initial data in $H^s\left({ℝ}^n\right)$ for $s>0$.