Scaling properties of functionals and existence of constrained minimizers

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Existence and orbital stability of standing waves for nonlinear Schr\"odinger systems (2015, background): “niques have been developed to prove strict subadditivity conditions. Most are based on some homogeneity type property. In autonomous case it is also possible to use scaling arguments, see for example [4,10,26]. In the case of multiple constraints how to establish strict subadditivity conditions is m”
Mass minimizers and concentration for nonlinear Choquard equations in $\R^N$ (2015, methodology): “ the function c→ Ip(c2) is continuous on (0,+∞); (2) Ip(c2) <Ip(α2)+Ip(c2 − α2), ∀ 0 <α<c<+∞. (2.7) Proof. The proof of (1) follows from Lemma 2.4 and is similar to that of Theorem 2.1 in [2], so we omit it. (2) For any c>0, let {un} ⊂ S(c) be a minimizing sequence for Ip(c2) <0, t”
Existence and instability of standing waves with prescribed norm for a class of Schrödinger–Poisson equations (2011, background): “In the case p ∈ (2, 10 3 ), the standing waves found in [4, 5, 30] by minimization are orbitally stable.”
Multiplicity of normalized solutions for a class of nonlinear Schrodinger-Poisson-Slater equations (2013, background): “t;0 o . (1.3) The parameter λc ∈ R, in this situation, is not ﬁxed any more and it appears as a Lagrange parameter. The above normalized problem associated to (Eλ), has been studied in the literature [8, 9, 10, 11, 15, 16, 26]. In the cited references, the existence and non-existence of normalized s”