265 citations · 1.7k across the 44 of their papers we have counts for
48 papers · 1 filter
Normalized solutions to mass supercritical Schrödinger equations with radial potentials
Pablo Carrillo, P. Carrillo, Louis Jeanjean +1
We study the stationary nonlinear Schrödinger equation \begin{equation}-Δu+V(x)u+λu=|u|^{q-2}u,\quad u \in H^1(\mathbb{R}^N), \quad N \geq 2\end{equation} where $V \in L^{\infty}(\…
Serrin-type Overdetermination in Scaling Limits: Sharp Existence and Asymptotic Behavior of Quasi-linear Schrödinger Energy Ground States
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
This paper establishes optimal existence results and limiting profiles for energy ground states of the quasi-linear Schrödinger equation $$ -Δu - Δ(|u|^{2})u + λu = |u|^{p-2}u \qua…
Normalized solutions of -supercritical NLS equations on noncompact metric graphs
Simone Dovetta, Louis Jeanjean, Enrico Serra
We consider the existence of normalized solutions to nonlinear Schrödinger equations on noncompact metric graphs in the supercritical regime. For sufficiently small prescribe…
Infinitely many normalized solutions of -supercritical NLS equations on noncompact metric graphs with localized nonlinearities
Pablo Carrillo, Damien Galant, Louis Jeanjean +1
We consider the existence of solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities. In an -supercritical regime, we establish…
Normalized ground states for a coupled Schrödinger system: Mass super-critical case
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
We consider the existence of solutions to systems of coupled Schrödinger equations $$ \begin{cases} -Δu+λ_1 u=μ_1 u^{p…
Normalized solutions of -supercritical NLS equations on noncompact metric graphs with localized nonlinearities
Jack Borthwick, Xiaojun Chang, Louis Jeanjean +1
In this paper we are concerned with the existence of normalized solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities. In a -…
Bounded Palais-Smale sequences with Morse type information for some constrained functionals
Jack Borthwick, Xiaojun Chang, Louis Jeanjean +1
In this paper, we study, for functionals having a mountain pass geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information.
Normalized solutions of -supercritical NLS equations on compact metric graphs
Xiaojun Chang, Louis Jeanjean, Nicola Soave
This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schrödinger equation on compact metric graphs. The invest…
A global branch approach to normalized solutions for the Schrödinger equation
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form \begin{equation*} -Δu+λu=g(u), \quad u \in H^1(\m…
Normalized solutions with positive energies for a coercive problem and application to the cubic-quintic nonlinear Schrödinger equation
Louis Jeanjean, Sheng-Sen Lu
In any dimension , for given mass and when the energy functional \begin{equation*} I(u) := \frac{1}{2} \int_{\mathbb{R}^N} |\nabla u|^2 dx - \int_{\mathbb{R…
On global minimizers for a mass constrained problem
Louis Jeanjean, Sheng-Sen Lu
In any dimension , for given mass and for the energy functional \begin{equation*} I(u):=\frac{1}{2}\int_{\mathbb{R}^N}|\nabla u|^2dx-\int_{\mathbb{R}^N}F(u)…
Logarithmic estimates for mean-field models in dimension two and the Schrödinger-Poisson system
Jean Dolbeault, Rupert L. Frank, Louis Jeanjean
In dimension two, we investigate a free energy and the ground state energy of the Schrödinger-Poisson system coupled with a logarithmic nonlinearity in terms of underlying function…
Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
Louis Jeanjean, Thanh Trung Le
We look for solutions to the Schrödinger-Poisson-Slater equation which satisfy \begin{…
Multiple normalized solutions for a Sobolev critical Schrödinger equation
Louis Jeanjean, Thanh Trung LE
We study the existence of standing waves, of prescribed -norm (the mass), for the nonlinear Schrödinger equation with mixed power nonlinearities $$ i \partial_t ϕ+ Δϕ+ μϕ|ϕ|^{…
Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation
Antonio J. Fernández, Louis Jeanjean, Rainer Mandel +1
We study the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy when the norm (the \textit{mass}) } is kept fixe…
Orbital stability of ground states for a Sobolev critical Schrödinger equation
Louis Jeanjean, Jacek Jendrej, Thanh Trung Le +1
We study the existence of ground state standing waves, of prescribed mass, for the nonlinear Schrödinger equation with mixed power nonlinearities \begin{equation*} i \partial_t v +…
A mass supercritical problem revisited
Louis Jeanjean, Sheng-Sen Lu
In any dimension and for given mass , we revisit the nonlinear scalar field equation with an constraint: $$ -Δu=f(u)-μu, \quad u \in H^1(\mathbb{R}^N) \quad \te…
Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases
Louis Jeanjean, Vicentiu D. Radulescu
We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated…
Some remarks on a minimization problem associated to a fourth order nonlinear Schrödinger equation
Nabile Boussaïd, Antonio J. Fernández, Louis Jeanjean
Let , , and . In the present paper, we study, for given, the constrained minimization problem \begin{equation*} \label{MinL2fixed} m(c):=…
Stationary waves with prescribed -norm for the planar Schrödinger-Poisson system
Silvia Cingolani, Louis Jeanjean
The paper deals with the existence of standing wave solutions for the Schrödinger-Poisson system with prescribed mass in dimension . This leads to investigate the existence of…
Nonradial normalized solutions for nonlinear scalar field equations
Louis Jeanjean, Sheng-Sen Lu
We study the following nonlinear scalar field equation Here $f\in C(\mathbb{…
Nonlinear scalar field equations with general nonlinearity
Louis Jeanjean, Sheng-Sen Lu
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -Δ{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where and …
A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient
Colette De Coster, Antonio J. Fernández, Louis Jeanjean
Let , , be a smooth bounded domain. We consider a boundary value problem of the form $$-Δu = c_λ(x) u + μ(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(…
Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation under the constr…