Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations

161 citations recorded by the source corpus.

How researchers see this paper

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

Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems (2013, background): “With the constant potentials, segregation was discussed for the repulsive case with β negatively large (for example, [4,7– 9,15,21,25,29,30]), while the uniqueness of positive radial solutions was proved for a large positive constant β [34].”
Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent: higher dimensional case (2015, unknown): “1) were introduced in [14,37].”
Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent (2012, background): “precise deﬁnition of β0 (see (4.2) in Section 4). In particular, if µ1 = µ2, then β0 = 2 N−2 max{µ1,µ2}. (2) For the case p= 2 and N ≤ 3, some uniqueness results about system (1.1) were introduced in [36]. However, their proofs heavily depend on p= 2, and so can not work here. Now, let us consider t”
Infinitely many positive solutions for nonlinear equations with non-symmetric potentials (2012, background): “10) (It has been proved in [47] that for β > max{μ1, μ2}, all solutions to (3.”