nonlinear schrödinger system
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scholarly journals The compactness of minimizing sequences for a nonlinear Schrödinger system with potentials

2021 ◽  
Author(s):  
Norihisa Ikoma ◽  
Yasuhito Miyamoto
Keyword(s):  
Minimizing Sequences ◽  
Minimizing Sequence ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

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.

scholarly journals Scattering for the Quadratic Nonlinear Schrödinger System in R5 without Mass-Resonance Condition

2021 ◽  
Vol 64 (3) ◽  
pp. 261-291
Author(s):  
Masaru Hamano ◽  
Takahisa Inui ◽  
Kuranosuke Nishimura
Keyword(s):  
Resonance Condition ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

scholarly journals Large Time Asymptotics for a Cubic Nonlinear Schrödinger System in One Space Dimension

2021 ◽  
Vol 64 (3) ◽  
pp. 361-377
Author(s):  
Chunhua Li ◽  
Yoshinori Nishii ◽  
Yuji Sagawa ◽  
Hideaki Sunagawa
Keyword(s):  
Large Time ◽  
Space Dimension ◽  
Large Time Asymptotics ◽  
Nonlinear Schrödinger ◽  
Time Asymptotics ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System ◽  
One Space Dimension

scholarly journals Ground State Solution for an Autonomous Nonlinear Schrödinger System

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Min Liu ◽  
Jiu Liu
Keyword(s):  
Ground State ◽  
Critical Sobolev Exponent ◽  
Growth Conditions ◽  
Ground State Solution ◽  
State Solution ◽  
Subcritical Growth ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Sobolev Exponent ◽  
Schrödinger System

In this paper, we study the following autonomous nonlinear Schrödinger system (discussed in the paper), where λ , μ , and ν are positive parameters; 2 ∗ = 2 N / N − 2 is the critical Sobolev exponent; and f satisfies general subcritical growth conditions. With the help of the Pohožaev manifold, a ground state solution is obtained.

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