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The forced non‐linear Schrödinger equation with a potential on the half‐line
Author(s) -
Weder Ricardo
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.637
Subject(s) - mathematics , half line , line (geometry) , mathematical analysis , geometry , boundary value problem
In this paper we prove that the initial‐boundary value problem for the forced non‐linear Schrödinger equation with a potential on the half‐line is locally and (under stronger conditions) globally well posed, i.e. that there is a unique solution that depends continuously on the force at the boundary and on the initial data. We allow for a large class of unbounded potentials. Actually, for local solutions we have no restriction on the growth at infinity of the positive part of the potential, and for global solutions very mild assumptions that allow, for example, for exponential growth. Copyright © 2005 John Wiley & Sons, Ltd.