Note on Ground States of Nonlinear Schrodinger Systems

By Thomas, Bartsch, Zhi-qiang, Wang. Journal of Partial Differential Equations, 2006

242 citations recorded by the source corpus.

We give sufficient and necessary conditions for the existence and nonexistence of positive ground state solutions of a class of coupled nonlinear Schrödinger equations.

Subfields: Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e73e08c9f111594f0fb444aa4ac008154a3e1ebe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Normalized solutions for a coupled Schrödinger system (2019, unknown): “[4, 11, 12, 14, 24, 25, 26, 29, 30, 31, 32, 34] and the references therein.”
Bound states for a coupled Schrödinger system (2007, background): “for existence of ground and bound state solutions, in particular [3, 6, 25, 29] giving an existence result for β in the large, a result in similar spirit to ours; and [23, 28, 33, 34] for multiplicity results and semiclassical states.”
Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems (2022, background): “We refer the reader to [1, 4, 6, 12, 13, 16, 17, 32, 38] and the references therein.”
Semiclassical states for weakly coupled nonlinear Schrödinger systems (2008, background): “Recently, this problem has been tackled in [2, 3, 7, 17, 18, 25] by different methods.”
Ground States and Bound States of a Nonlinear Schrödinger System (2010, background): “Schrödinger systems, nonlinear couplings, co-existing ground states, multiple bound states”
Positive solutions for a weakly coupled nonlinear Schrödinger system (2006, result): “After this work was completed, we became aware of [4,5] in which there are some results related to ours and of [8,30] also concerning this subject.”
Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations (2011, unknown): “(See [3] and [4].”
Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems (2013, background): “1 the requirement of β / ∈ (min{μ, ν},max{μ, ν}) is necessary as there is a non-existence result on positive solutions (for example, [5]), and in particular there are no positive solutions when P = Q for such β.”
A natural constraint approach to normalized solutions of nonlinear Schr\"odinger equations and systems (2016, background): “[2,10,15,25,28,29,31,38,40,41,42,51,53] and the references therein, while problem (1.”