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ASYMPTOTICALLY LINEAR SOLUTIONS IN H<sup>1</sup> OF THE 2-D DEFOCUSING NONLINEAR SCHRöDINGER AND HARTREE EQUATIONS
In the 2-d setting, given an H 1 solution v(t) to the linear Schrödinger equation i∂ t v + Δ v = 0, we prove the existence (but not uniqueness) of an H 1 solution u(t) to the defocusing nonlinear Schrödinger (NLS) equation i∂ t u + Δu -|u| p-1 …