Positive solutions for a weakly coupled nonlinear Schrödinger system

By L. Maia, Eugenio Montefusco, Benedetta Pellacci. 2006

385 citations recorded by the source corpus.

Abstract Existence of a nontrivial solution is established, via variational methods, for a system of weakly coupled nonlinear Schrodinger equations. The main goal is to obtain a positive solution, of minimal action if possible, with all vector components not identically zero. Generalizations for nonautonomous systems are considered.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d23c0e23fb54c3f29441eb382efa531143ca6fb6

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In Applied Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

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.”
Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations (2007, background): “The case in which the coupling is nonlinear has been studied in [5, 18 , 21, 22], see also [4, 16].”
Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations (2008, background): “If µj > 0 as considered here, we are dealing with an attractive self-interaction of the single states |j〉, j = 1, 2.”
Minimal energy solutions for cooperative nonlinear Schrödinger systems (2015, background): “1 in [11] we know that for all b ≥ 0 a nonnegative minimizer of I|Nb exists which, by Lemma 3.”
Multiple positive normalized solutions for nonlinear Schrödinger systems (2017, background): “1) where (λ1,λ2) are given has been, starting from the pioneering papers [2, 13, 27, 30, 36], the subject of a huge literature in the recent years.”
Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent (2012, background): “In the subcritical case p < 2∗/2, the existence of solutions have received great interest recently, see [4, 7, 18, 24, 25, 27, 29, 34] and references therein.”
Uniqueness of Positive Solutions for a Nonlinear Elliptic System (2009, background): “We refer to [1,3,6,8–10,13,14] and references therein.”
Ground States and Bound States of a Nonlinear Schrödinger System (2010, methodology): “In the case of the 2-system (there is only one coupling constant β := β12 = β21), in [2, 3, 5, 6, 20, 26] more precise estimates on the size of a β0 have been given to assure for β > β0 the existence of a nontrivial ground state solution.”
Semiclassical states for weakly coupled nonlinear Schrödinger systems (2008, background): “[10], [18]) that the functionsφz, ψz are radially symmetric, nonnegative, and decay exponentially to zero at infinity.”