On some semilinear equations of Schrödinger type

Authors

  • Rossella Agliardi
  • Daniela Mari

DOI:

https://doi.org/10.7146/math.scand.a-14366

Abstract

We study the initial value problem for some semilinear pseudo-differential equations of the form $\partial _tu + i\ H(x,D_x)u = F(u,\nabla u)$. 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.

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Published

2002-03-01

Issue

Vol. 90 No. 1 (2002)

Section

Articles

How to Cite

[1]
R. Agliardi and D. Mari, “On some semilinear equations of Schrödinger type”, Math. Scand., vol. 90, no. 1, pp. 139–151, Mar. 2002, doi: 10.7146/math.scand.a-14366.