On some semilinear equations of Schrödinger type

Rossella Agliardi, Daniela Mari

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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DOI: http://dx.doi.org/10.7146/math.scand.a-14366

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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