Ontology type: schema:ScholarlyArticle
1995-12
AUTHORS ABSTRACT
We consider the nonlinear Schrödinger equation (NLS) (see below) with a general “potential”F(u), for which there are in general no conservation laws. The main assumption onF(u) is a growth rateO(|u|k) for large |u|, in addition to some smoothness depending on the problem considered. A uniqueness theorem is proved with minimal smoothness assumption onF andu, which is useful in eliminating the “auxiliary conditions” in many cases. A new local existence theorem forHS-solutions is proved using an auxiliary space of Lebesgue type (rather than Besov type); here the main assumption is thatk≤1+4/(m−2s) ifs
281-306
http://scigraph.springernature.com/pub.10.1007/bf02787794
DOIhttp://dx.doi.org/10.1007/bf02787794
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