Zobrazeno 1 - 10
of 256
pro vyhledávání: '"Yan, Shusen"'
Let $\Omega\subset\mathbb{R}^N$ be a smooth bounded domain with $N\ge2$ and $\Omega_\epsilon=\Omega\backslash B(P,\epsilon)$ where $B(P,\epsilon)$ is the ball centered at $P\in\Omega$ and radius $\epsilon$. In this paper, we establish the number, loc
Externí odkaz:
http://arxiv.org/abs/2202.10895
Publikováno v:
In Journal of Differential Equations 25 December 2024 413:462-496
We consider the following nonlinear problem $$ (P) \quad \quad - \Delta u + V(|y|)u=u^{p},\quad u>0 \quad \mbox{in} \ {\mathbb{R}}^N, \quad u \in H^1({\mathbb{R}}^N), $$ where $V(r)$ is a positive function, $1
Externí odkaz:
http://arxiv.org/abs/2106.15431
We consider the following prescribed scalar curvature equations in ${\mathbb{R}}^N$ $$ - \Delta u =K(|y|)u^{2^*-1},\quad u>0 \quad \mbox{in} \quad {\mathbb{R}}^N, \quad u \in D^{1, 2}({\mathbb{R}}^N), $$ where $K(r)$ is a positive function, $2^*=\fra
Externí odkaz:
http://arxiv.org/abs/2106.15423
Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two
We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -\Delta u=u^{p} &{\text{in}~\Omega},\\[0.5mm] u>0 &{\text{in}~\Omega},\\[0.5mm] u=0 &{\text{on}~\partial \Omega}, \end{cases} \end{equation*} where $\Omega\subset \mathbb R^
Externí odkaz:
http://arxiv.org/abs/2102.09523
We study the Bose-Einstein condensates (BEC) in two or three dimensions with attractive interactions, described by $L^{2}$ constraint Gross-Pitaevskii energy functional. First, we give the precise description of the chemical potential of the condensa
Externí odkaz:
http://arxiv.org/abs/1909.08828
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In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \begin{equation*} \left\{\begin{array}{rlll} -\Delta u&=|u|^{\frac{4}{N-2}}u, &\hbox{ in }\Omega,\\ u&=0, &\hbox{ on }\partial\Omega. \end{array}\righ
Externí odkaz:
http://arxiv.org/abs/1804.01687
Publikováno v:
In Journal of Functional Analysis 15 November 2022 283(10)
Publikováno v:
In Journal of Differential Equations 25 July 2022 326:254-279