TY - JOUR AU - Agliardi, Rossella AU - Mari, Daniela PY - 2002/03/01 Y2 - 2024/03/28 TI - On some semilinear equations of Schrödinger type JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 90 IS - 1 SE - Articles DO - 10.7146/math.scand.a-14366 UR - https://www.mscand.dk/article/view/14366 SP - 139-151 AB - We study the initial value problem for some semilinear pseudo-differential equations of the form $\partial _tu + i\ H(x,D_x)u = F(u, abla u)$. The assumptions we make on $H$ are trivially satisfied by $\Delta$, thus our equations generalize Schrdinger type equations. A local existence theorem is proved in some weighted Sobolev spaces. ER -