Multiple normalized solutions for quasi-linear Schr\"odinger equations
By Louis Jeanjean, Tingjian Luo, Zhi-Qiang Wang. 2014
121 citations recorded by the source corpus.
In this paper we prove the existence of two solutions having a prescribed $L^2$-norm for a quasi-linear Schr\"odinger equation. One of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global. To overcome the lack of differentiability of the associated functional, we rely on a perturbation method developed in [27].
Subfields: Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f1a18ca41be118bd2eb7cdec3be84a84815ebbe2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
In Mathematical Physics
- Gianmaria Verzini
- Hugo Tavares
- Benedetta Noris
- Nicola Soave
- Thomas Bartsch
- Bernard Helffer
- Louis Jeanjean
Citations in the corpus
- Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case (2019, unknown): “More recently, this kind of idea has been exploited and further developed in other contexts, and more in general the search for normalized solutions in cases when the energy is unbounded from below on the L-constraint attracted much attention: we refer to [1, 7, 12, 13, 16, 20, 34] for normalized so”
- Existence and orbital stability of the ground states with prescribed mass for the $L^2$-critical and supercritical NLS on bounded domains (2013, background): “On the other hand, NLS on RN with a nonhomogeneous nonlinearity cannot be treated in this way, and the fixed mass problem becomes hard to tackle [Bellazzini et al. 2013; Bartsch and de Valeriola 2013; Jeanjean 1997; Jeanjean et al. 2014].”
- Normalized ground states for the NLS equation with combined nonlinearities (2018, unknown): “More recently, however, problems of this type received much attention, see [1, 10–12, 15, 16, 32] for normalized solutions to scalar equations in the whole space R , [6–9, 28] for normalized solutions to systems”