Zobrazeno 1 - 10
of 875
pro vyhledávání: '"Jeanjean P"'
We consider the existence of normalized solutions to nonlinear Schr\"odinger equations on noncompact metric graphs in the $L^2$ supercritical regime. For sufficiently small prescribed mass ($L^2$ norm), we prove existence of positive solutions on two
Externí odkaz:
http://arxiv.org/abs/2404.15841
We consider the existence of solutions for nonlinear Schr\"odinger equations on noncompact metric graphs with localized nonlinearities. In an $L^2$-supercritical regime, we establish the existence of infinitely many solutions for any prescribed mass.
Externí odkaz:
http://arxiv.org/abs/2403.10959
We consider the existence of solutions $(\lambda_1,\lambda_2, u, v)\in \mathbb{R}^2\times (H^1(\mathbb{R}^N))^2$ to systems of coupled Schr\"odinger equations $$ \begin{cases} -\Delta u+\lambda_1 u=\mu_1 u^{p-1}+\beta r_1 u^{r_1-1}v^{r_2}\quad &\hbox
Externí odkaz:
http://arxiv.org/abs/2311.10994
Autor:
Marine Mondino, Cécilia Neige, Jean-Marie Batail, Noomane Bouaziz, Maxime Bubrovszky, Samuel Bulteau, Anastasia Demina, Ludovic C. Dormegny-Jeanjean, Ghina Harika-Germaneau, Dominique Januel, Charles Laidi, Virginie Moulier, Marion Plaze, Arnaud Pouchon, Emmanuel Poulet, Maud Rothärmel, Anne Sauvaget, Antoine Yrondi, David Szekely, Jerome Brunelin
Publikováno v:
Frontiers in Psychiatry, Vol 15 (2024)
Over the past three decades, non-invasive brain stimulation (NIBS) techniques have gained worldwide attention and demonstrated therapeutic potential in various medical fields, particularly psychiatry. The emergence of these novel techniques has led t
Externí odkaz:
https://doaj.org/article/d02573f18d61441d9af1ab9eefc5243b
In this paper we are concerned with the existence of normalized solutions for nonlinear Schr\"odinger equations on noncompact metric graphs with localized nonlinearities. In a $L^2$-supercritical regime, we obtain the existence of solutions for any p
Externí odkaz:
http://arxiv.org/abs/2212.04840
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.
Comment: This version is the final one, corresponding to the paper n
Comment: This version is the final one, corresponding to the paper n
Externí odkaz:
http://arxiv.org/abs/2210.12626
This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schr\"odinger equation on compact metric graphs. The investigation is based upon a general variational principle which combines
Externí odkaz:
http://arxiv.org/abs/2204.01043
We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schr\"odinger equation of the form \begin{equation*} -\Delta u+\lambda u=g(u), \quad u \in H^1(\mathbb{R}^N), \, N \geq 1. \end{equation*} Our approach
Externí odkaz:
http://arxiv.org/abs/2112.05869
Autor:
Jeanjean, Louis, Lu, Sheng-Sen
Publikováno v:
Mathematical Models and Methods in Applied Sciences 32 (2022) 1557-1588
In any dimension $N \geq 1$, for given mass $m > 0$ and when the $C^1$ energy functional \begin{equation*} I(u) := \frac{1}{2} \int_{\mathbb{R}^N} |\nabla u|^2 dx - \int_{\mathbb{R}^N} F(u) dx \end{equation*} is coercive on the mass constraint \begin
Externí odkaz:
http://arxiv.org/abs/2111.13020
Autor:
Jeanjean, Louis, Lu, Sheng-Sen
Publikováno v:
Calculus of Variations and Partial Differential Equations, 61 (2022): 214
In any dimension $N \geq 1$, for given mass $m > 0$ and for the $C^1$ energy functional \begin{equation*} I(u):=\frac{1}{2}\int_{\mathbb{R}^N}|\nabla u|^2dx-\int_{\mathbb{R}^N}F(u)dx, \end{equation*} we revisit the classical problem of finding condit
Externí odkaz:
http://arxiv.org/abs/2108.04142