Zobrazeno 1 - 10
of 404
pro vyhledávání: '"35J91"'
Autor:
Hou, Songbo, Kong, Xiaoqing
In this paper, we study a generalized self-dual Chern-Simons equation on the lattice graph $\mathbb{Z}^n$ for $n \geq 2$ as given by \[ \Delta u = \lambda e^u (e^u - 1)^{2p+1} + 4\pi \sum_{j=1}^M n_j \delta_{p_j}, \] where $\Delta$ denotes the Laplac
Externí odkaz:
http://arxiv.org/abs/2410.18407
Autor:
Schino, Jacopo, Smyrnelis, Panayotis
Given $m \in \mathbb{N} \setminus \{0\}$ and $\rho > 0$, we find solutions $(\lambda,u)$ to the problem \begin{equation*} \begin{cases} \bigl(-\frac{\mathrm{d}^2}{\mathrm{d} x^2}\bigr)^m u + \lambda G'(u) = F'(u)\\ \int_{\mathbb{R}} K(u) \, \mathrm{d
Externí odkaz:
http://arxiv.org/abs/2410.03318
Autor:
Huan, Ling, Romani, Giulio
We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser. For all prescribed values of the mass, we prove existence of a positiv
Externí odkaz:
http://arxiv.org/abs/2407.20618
We consider the planar Taylor-Couette system for the steady motion of a viscous incompressible fluid in the region between two concentric disks, the inner one being at rest and the outer one rotating with constant angular speed. We study the uniquene
Externí odkaz:
http://arxiv.org/abs/2406.14960
Autor:
Sun, Liming, Wang, Lei
We consider a type of Hardy-Sobolev inequality, whose weight function is singular on the whole domain boundary. We are concerned with the attainability of the best constant of such inequality. In dimension two, we link the inequality to a conformally
Externí odkaz:
http://arxiv.org/abs/2405.09795
We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension $d = 4$. We determine the exponent governing the probability to hit a small ball with an exceptio
Externí odkaz:
http://arxiv.org/abs/2312.00711
For a function $F: X \to Y$ between real Banach spaces, we show how continuation methods to solve $F(u) = g$ may improve from basic understanding of the critical set $C$ of $F$. The algorithm aims at special points with a large number of preimages, w
Externí odkaz:
http://arxiv.org/abs/2311.10494
We consider the following higher order prescribed curvature problem on $ {\mathbb{S}}^N : $ \begin{equation*} D^m \tilde u=\widetilde{K}(y) \tilde u^{m^{*}-1} \quad \mbox{on} \ {\mathbb {S}}^N, \qquad \tilde u >0 \quad \mbox{in} \ {\mathbb {S}}^N. \e
Externí odkaz:
http://arxiv.org/abs/2308.07945
We study normalised solutions of the stationary Gross-Pitaevskii-Poisson (GPP) equation with a defocusing local nonlinear term, $$-\Delta u+\lambda u+|u|^2u =(I_\alpha*|u|^2)u\quad\text{in $\mathbb R^3$},\qquad\int_{\mathbb R^3}u^2dx=\rho^2,$$ where
Externí odkaz:
http://arxiv.org/abs/2308.04527
Autor:
Wolansky, Gershon
The Choquard equation is a partial differential equation that has gained significant interest and attention in recent decades. It is a nonlinear equation that combines elements of both the Laplace and Schr\"odinger operators, and it arises frequently
Externí odkaz:
http://arxiv.org/abs/2307.00948