scholarly journals On the least energy sign-changing solutions for a nonlinear elliptic system

2015 ◽  
Vol 35 (5) ◽  
pp. 2151-2164 ◽  
Author(s):  
Yohei Sato ◽  
◽  
Zhi-Qiang Wang ◽  
Keyword(s):  
Elliptic System ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions ◽  
Least Energy

On Some Generalized Compound Problem for a Nonlinear Elliptic System

1986 ◽  
Vol 126 (1) ◽  
pp. 55-62
Author(s):  
J. Wolska-Bochenek ◽  
L. Von Wolfersdorf
Keyword(s):  
Elliptic System ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic

Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings

2015 ◽  
Vol 15 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Yohei Sato ◽  
Zhi-Qiang Wang
Keyword(s):  
Ground State ◽  
Nonlinear Elliptic System ◽  
Ground State Solutions ◽  
Nonlinear Elliptic ◽  
Asymptotic Profile ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems ◽  
Bose Einstein ◽  
Least Energy Solutions ◽  
Least Energy

AbstractIn this paper we study the ground state solutions for a nonlinear elliptic system of three equations which comes from models in Bose-Einstein condensates. Comparing with existing works in the literature which have been on purely attractive or purely repulsive cases, our investigation focuses on the effect of mixed interaction of attractive and repulsive couplings. We establish the existence of least energy positive solutions and study asymptotic profile of the ground state solutions, giving indication of co-existence of synchronization and segregation. In particular we show symmetry breaking for the ground state solutions.

scholarly journals Existence of Nontrivial Solutions for Perturbed Elliptic System inℝN

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Juan Jiang
Keyword(s):  
Variational Method ◽  
Critical Exponent ◽  
Elliptic System ◽  
Existence Result ◽  
Nonlinear Elliptic System ◽  
Nontrivial Solutions ◽  
Nonlinear Elliptic ◽  
Sobolev Critical Exponent

We consider the perturbed nonlinear elliptic system-ε2Δu+V(x)u=K(x)|u|2*-2u+Hu(u,v),  x∈ℝN,-ε2Δv+V(x)v=K(x)|v|2*-2v+Hv(u,v),  x∈ℝN, whereN≥3,2*=2N/(N-2)is the Sobolev critical exponent. Under proper conditions onV,H, andK, the existence result and multiplicity of the system are obtained by using variational method providedεis small enough.

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