Standing waves with a critical frequency for a quasilinear Schrödinger equation
2019 ◽
Vol 22
(08)
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pp. 1950070
Keyword(s):
We consider the following quasilinear Schrödinger equation [Formula: see text] where [Formula: see text], [Formula: see text], and [Formula: see text] satisfies a weaker growth condition than the Ambrosetti–Rabinowitz type condition in Byeon and Wang [Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal. 165(4) (2002) 295–316; Standing waves with a critical frequency for nonlinear Schrödinger equations, II, Calc. Var. 18(2) (2003) 207–219]. We obtain the existence of the localized bound state solutions concentrating at an isolated component of the local minimum of [Formula: see text] and whose amplitude goes to 0 as [Formula: see text].
2004 ◽
Vol 203
(2)
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pp. 292-312
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2010 ◽
Vol 27
(4)
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pp. 1121-1152
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2008 ◽
Vol 360
(07)
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pp. 3813-3838
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2000 ◽
Vol 33
(21)
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pp. 3947-3949
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Existence of Multi-bump Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations
2005 ◽
Vol 29
(11-12)
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pp. 1877-1904
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2002 ◽
Vol 165
(4)
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pp. 295-316
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2000 ◽
Vol 51
(3)
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pp. 498-503
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