Tootfinder

Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case
Liejun Shen, Marco Squassina
https://arxiv.org/abs/2403.18014

Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case
We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schrödinger systems \[ \left\{ \begin{array}{ll} \displaystyle -Δu +A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \newline \displaystyle \partial_1A_2-\partial_2A_1=-\frac{1}{2}|u|^2,~\partial_1A_1+\partial_2A_2=0, \newline \displaystyle \partial_1A_0=A_2|u|^2,~ \partial_2A_0=-A_1|u|^2, \end{array} \right. \] where $a:\mathbb R^2\to\mathbb R^+$ is…

On tori periods of Weil representations of unitary groups
Neelima Borade, Jonas Franzel, Johannes Girsch, Wei Yao, Qiyao Yu, Elad Zelingher
https://arxiv.org/abs/2402.16808

On tori periods of Weil representations of unitary groups
We determine the restriction of Weil representations of unitary groups to maximal tori. In the local case, we show that the Weil representation contains a pair of compatible characters if and only if a root number condition holds. In the global case, we show that a tori period corresponding to a maximal anisotropic torus of the global theta lift of a character does not vanish if and only if the local condition is satisfied everywhere and a central value of an $L$-function does not vanish. Our p…

Abgeordnete fordern Sanktionen nach Nawalny-Tod
Nach dem Tod des Kreml-Kritikers Alexej Nawalny haben Bundestagsabgeordnete der Ampel und der Union schärfere Sanktionen gegen Russland gefordert. "Wir fordern weitere Sanktionen für das russische Regime und müssen alles tun, um der Ukraine zum Sieg zu verhelfen", sagte der SPD-Politiker Frank Schwabe.
CDU-Außenpolitiker Norbert Röttgen forderte, die deutsche Unterstützung der U…
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Ukraine-Liveblog: ++ Wohl keine EU-Beitrittsgespräche vor Europawahl ++
EU-Kommissionspräsidentin von der Leyen rechnet vor den Europawahlen nicht mit Beitrittsgesprächen mit der Ukraine. Innenkommissarin Johansson lobt Deutschland für das Engagement bei der Aufnahme von Geflüchteten. Der Liveblog vom Mittwoch zum Nachlesen.

Multiple normalized solutions to a system of nonlinear Schr\"{o}dinger equations
Jaros{\l}aw Mederski, Andrzej Szulkin
https://arxiv.org/abs/2403.16987

Multiple normalized solutions to a system of nonlinear Schrödinger equations
We find a normalized solution $u=(u_1,\ldots,u_K)$ to the system of $K$ coupled nonlinear Schrödinger equations \begin{equation*} \left\{ \begin{array}{l} -Δu_i+ λ_i u_i = \sum_{j=1}^Kβ_{i,j}u_i|u_i|^{p/2-2}|u_j|^{p/2} \quad \mathrm{in} \, \mathbb{R}^3,\newline u_i \in H^1_{rad}(\mathbb{R}^3),\newline \int_{\mathbb{R}^3} |u_i|^2 \, dx = ρ_i^2 \quad \text{for }i=1,\ldots, K, \end{array} \right. \end{equation*} where $ρ=(ρ_1,\ldots,ρ_K)\in(0,\infty)…

A sweater label. Makes sense, but I've seen "rabbit hair" mostly in coats, hats, and such; not in sweaters, definitely not in Loft branded sweaters.
I'm guessing this is an expensive sweater.
#apparel #clothing

Existence and concentration of normalized solutions for $p$-Laplacian equations with logarithmic nonlinearity
Liejun Shen, Marco Squassina
https://arxiv.org/abs/2403.09366

Existence and concentration of normalized solutions for $p$-Laplacian equations with logarithmic nonlinearity
We investigate the existence and concentration of normalized solutions for a $p$-Laplacian problem with logarithmic nonlinearity of type \[ \left\{ \begin{array}{ll} \displaystyle -\varepsilon^pΔ_p u+V(x)|u|^{p-2}u=λ|u|^{p-2}u+|u|^{p-2}u\log|u|^p ~\text{in}~\mathbb R^N,\newline \displaystyle \int_{\mathbb R^N}|u|^pdx=a^p\varepsilon^N, \end{array} \right. \] where $a,\varepsilon> 0$, $λ\in\mathbb R$ is known as the Lagrange multipl…