Abstract

From the introduction: We consider the first initial boundary value problem for Schrödinger systems \[ (-1)^{m-1}iL(x,t,D)u-u_t=f(x,t), \quad L(x,t,D)=\sum D^p\bigl(a_{pq}(x,t)D^q\bigr) \] in an infinite cylinder \(Q_\infty=\Omega\times (0,\infty)\). We will prove some results on the existence and uniqueness of generalized solutions of the problem in the space \({\overset\circ H}_\gamma^{m,0}(Q_\infty)\) for \(\gamma >0\) big enough.