On some semilinear equations of Schrödinger type
AbstractWe study the initial value problem for some semilinear pseudo-differential equations of the form $\partial _tu + i\ H(x,D_x)u = F(u,\nabla u)$. 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.
How to Cite
Agliardi, R., & Mari, D. (2002). On some semilinear equations of Schrödinger type. MATHEMATICA SCANDINAVICA, 90(1), 139-151. https://doi.org/10.7146/math.scand.a-14366