scholarly journals Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents

2019 ◽  
Vol 18 (5) ◽  
pp. 2693-2715
Author(s):  
Yongpeng Chen ◽  
◽  
Yuxia Guo ◽  
Zhongwei Tang ◽  
Keyword(s):  
Critical Exponents ◽  
Ground State ◽  
Ground State Solutions ◽  
Schrödinger Systems ◽  
Quasilinear Schrödinger Systems

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.

Ground state solutions of Hamiltonian elliptic systems in dimension two

2019 ◽  
Vol 150 (4) ◽  
pp. 1737-1768 ◽  
Author(s):  
Djairo G. de Figueiredo ◽  
João Marcos do Ó ◽  
Jianjun Zhang
Keyword(s):  
Elliptic System ◽  
Ground State ◽  
Elliptic Systems ◽  
Nehari Manifold ◽  
Existence Results ◽  
Ground State Solutions ◽  
Variational Framework ◽  
Hamiltonian Elliptic System ◽  
Schrödinger Systems ◽  
Image Position

AbstractThe aim of this paper is to study Hamiltonian elliptic system of the form 0.1$$\left\{ {\matrix{ {-\Delta u = g(v)} & {{\rm in}\;\Omega,} \cr {-\Delta v = f(u)} & {{\rm in}\;\Omega,} \cr {u = 0,v = 0} & {{\rm on}\;\partial \Omega,} \cr } } \right.$$ where Ω ⊂ ℝ2 is a bounded domain. In the second place, we present existence results for the following stationary Schrödinger systems defined in the whole plane 0.2$$\left\{ {\matrix{ {-\Delta u + u = g(v)\;\;\;{\rm in}\;{\open R}^2,} \cr {-\Delta v + v = f(u)\;\;\;{\rm in}\;{\open R}^2.} \cr } } \right.$$We assume that the nonlinearities f, g have critical growth in the sense of Trudinger–Moser. By using a suitable variational framework based on the generalized Nehari manifold method, we obtain the existence of ground state solutions of both systems (0.1) and (0.2).

scholarly journals Ground State Solutions for Schrödinger Problems with Magnetic Fields and Hardy-Sobolev Critical Exponents

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Min Liu ◽  
Xiaorui Yue
Keyword(s):  
Magnetic Fields ◽  
Schrödinger Equation ◽  
Critical Exponents ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solutions

A Schrödinger equation and system with magnetic fields and Hardy-Sobolev critical exponents are investigated in this paper, and, under proper conditions, the existence of ground state solutions to these two problems is given.

Quasilinear elliptic problems with critical exponents and Hardy terms in ℝN

2010 ◽  
Vol 53 (1) ◽  
pp. 175-193 ◽  
Author(s):  
Dongsheng Kang
Keyword(s):  
Variational Methods ◽  
Elliptic Problem ◽  
Critical Exponents ◽  
Ground State ◽  
Elliptic Problems ◽  
Ground State Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractWe deal with a singular quasilinear elliptic problem, which involves critical Hardy-Sobolev exponents and multiple Hardy terms. Using variational methods and analytic techniques, the existence of ground state solutions to the problem is obtained.

Concentration of Positive Ground State Solutions for Schrödinger–Maxwell Systems with Critical Growth

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Minbo Yang
Keyword(s):  
Critical Exponents ◽  
Ground State ◽  
Critical Growth ◽  
Maxwell System ◽  
Ground State Solutions

AbstractIn this paper, we study the following Schrödinger–Maxwell system with critical exponents inUnder suitable assumptions on the potentials

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