On some semilinear equations of Schrödinger type - Agliardi, Rossella; Mari, Daniela (Mathematica Scandinavica, 2002)
We study the initial value problem for some semilinear pseudo-differential equations of the form _tu + i H(x,D_x)u = F(u, abla u). The assumptions we make on H are trivially satisfied by Δ, thus our equations generalize Schrdinger type equations. A local existence theorem is proved in some weighted Sobolev spaces.