The compactness of minimizing sequences for a nonlinear Schrödinger system with potentials
Keyword(s):
In this paper, we consider the following minimizing problem with two constraints: [Formula: see text] where [Formula: see text] and [Formula: see text] is defined by [Formula: see text] [Formula: see text] Here [Formula: see text], [Formula: see text] and [Formula: see text] [Formula: see text] are given functions. For [Formula: see text], we consider two cases: (i) both of [Formula: see text] and [Formula: see text] are bounded, (ii) one of [Formula: see text] and [Formula: see text] is bounded. Under some assumptions on [Formula: see text] and [Formula: see text], we discuss the compactness of any minimizing sequence.
2016 ◽
Vol 57
(10)
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pp. 101501
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2013 ◽
Vol 31
(1)
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pp. 188
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