Abstract:We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution $$u=0$$
u
=
0
is the only solution for which the assumptions $$u(t=0)\vert _{D}=0, u(t=T)\vert _{D}=0$$
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