Normalized ground states for the NLS equation with combined nonlinearities

N Soave - Journal of Differential Equations, 2020 - Elsevier
We study existence and properties of ground states for the nonlinear Schrödinger equation
with combined power nonlinearities− Δ u= λ u+ μ| u| q− 2 u+| u| p− 2 u in RN, N≥ 1, having …

Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case

N Soave - Journal of Functional Analysis, 2020 - Elsevier
We study existence and properties of ground states for the nonlinear Schrödinger equation
with combined power nonlinearities− Δ u= λ u+ μ| u| q− 2 u+| u| 2⁎− 2 u in RN, N≥ 3, having …

Multiple normalized solutions for a Sobolev critical Schrödinger equation

L Jeanjean, TT Le - Mathematische Annalen, 2022 - Springer
We study the existence of standing waves, of prescribed L 2-norm (the mass), for the
nonlinear Schrödinger equation with mixed power nonlinearities i∂ t ϕ+ Δ ϕ+ μ ϕ| ϕ| q-2+ …

Normalized solutions to the fractional Schrödinger equations with combined nonlinearities

H Luo, Z Zhang - Calculus of Variations and Partial Differential …, 2020 - Springer
We study the normalized solutions of the fractional nonlinear Schrödinger equations with
combined nonlinearities (-Δ)^ su= λ u+ μ| u|^ q-2 u+| u|^ p-2 u\quad in~ R^ N,(-Δ) su= λ u+ μ …

A mass supercritical problem revisited

L Jeanjean, SS Lu - Calculus of Variations and Partial Differential …, 2020 - Springer
In any dimension N ≥ 1 N≥ 1 and for given mass m> 0 m> 0, we revisit the nonlinear scalar
field equation with an L^ 2 L 2 constraint:{-Δ u&= f (u)-μ u\quad in~ R^ N,\‖ u ‖^ 2_ L^ 2 …

Normalized solutions for a Schrödinger equation with critical growth in

CO Alves, C Ji, OH Miyagaki - Calculus of Variations and Partial …, 2022 - Springer
In this paper we study the existence of normalized solutions to the following nonlinear
Schrödinger equation with critical growth-Δ u= λ u+ f (u), in RN, u> 0,∫ RN| u| 2 dx= a 2 …

Orbital stability of ground states for a Sobolev critical Schrödinger equation

L Jeanjean, J Jendrej, TT Le, N Visciglia - Journal de Mathématiques Pures …, 2022 - Elsevier
We study the existence of ground state standing waves, of prescribed mass, for the
nonlinear Schrödinger equation with mixed power nonlinearities i∂ t v+ Δ v+ μ v| v| q− 2+ v …

Normalized solutions of mass supercritical Schrödinger equations with potential

T Bartsch, R Molle, M Rizzi, G Verzini - Communications in Partial …, 2021 - Taylor & Francis
This paper is concerned with the existence of normalized solutions of the nonlinear
Schrödinger equation− Δ u+ V (x) u+ λ u=| u| p− 2 u in RN in the mass supercritical and …

Normalized solutions for a coupled Schrödinger system

T Bartsch, X Zhong, W Zou - Mathematische Annalen, 2021 - Springer
In the present paper, we prove the existence of solutions (λ _1, λ _2, u, v) ∈ R^ 2 * H^ 1 (R^
3, R^ 2)(λ 1, λ 2, u, v)∈ R 2× H 1 (R 3, R 2) to systems of coupled Schrödinger equations-Δ …

Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation

L Jeanjean, TT Le - Journal of Differential Equations, 2021 - Elsevier
We look for solutions to the Schrödinger-Poisson-Slater equation (0.1)− Δ u+ λ u− γ (| x|− 1⁎|
u| 2) u− a| u| p− 2 u= 0 in R 3, which satisfy‖ u‖ L 2 (R 3) 2= c for some prescribed c> 0 …