scholarly journals Positive least energy solutions for k-coupled Schrödinger system with critical exponent: the higher dimension and cooperative case

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Xin Yin ◽  
Wenming Zou
Keyword(s):  
Critical Exponent ◽  
Higher Dimension ◽  
Coupled Schrödinger System ◽  
Least Energy Solutions ◽  
Least Energy ◽  
Schrödinger System

Existence of positive solutions to a linearly coupled Schrödinger system with critical exponent

2018 ◽  
Vol 20 (07) ◽  
pp. 1750082 ◽  
Author(s):  
Huiling Wu ◽  
Jianqing Chen ◽  
Yongqing Li
Keyword(s):  
Critical Exponent ◽  
Positive Solution ◽  
Positive Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrodinger Equations ◽  
Existence Of Positive Solutions ◽  
Schrödinger System

We are concerned with the system of nonlinear Schrödinger equations [Formula: see text] The existence of a positive solution to the system is proved.

scholarly journals Ground state solution of semilinear Schrödinger system with local super-quadratic conditions

2021 ◽  
pp. 1-18
Author(s):  
Jing Chen ◽  
Yiqing Li
Keyword(s):  
Variational Method ◽  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
The Other ◽  
Ground State Solutions ◽  
Approximation Argument ◽  
Least Energy Solutions ◽  
Least Energy ◽  
Schrödinger System

In this paper, we dedicate to studying the following semilinear Schrödinger system equation*-Δu+V1(x)u=Fu(x,u,v)amp;mboxin~RN,r-Δv+V2(x)v=Fv(x,u,v)amp;mboxin~RN,ru,v∈H1(RN),endequation* where the potential Vi are periodic in x,i=1,2, the nonlinearity F is allowed super-quadratic at some x ∈ R N and asymptotically quadratic at the other x ∈ R N . Under a local super-quadratic condition of F, an approximation argument and variational method are used to prove the existence of Nehari–Pankov type ground state solutions and the least energy solutions.

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