Zobrazeno 1 - 10
of 326
pro vyhledávání: '"Véron, Laurent"'
Autor:
Li, Yimei, Véron, Laurent
We study the local properties of positive solutions of the equation $-\Delta u+ae^{bu}=m|\nabla u|^q$ in a punctured domain $\Omega\setminus\{0\}$ of $\bf R^2$ where $m,a,b$ are positive parameters and $q>1$. We study particularly the existence of so
Externí odkaz:
http://arxiv.org/abs/2408.14246
Autor:
Chen, Huyuan, Véron, Laurent
Let $\lnlap$ be the logarithmic Laplacian operator with Fourier symbol $2\ln |\zeta|$, we study the expression of the diffusion kernel which is associated to the equation $$\partial_tu+ \lnlap u=0 \ \ {\rm in}\ \, (0,\tfrac N2) \times \R^N,\quad\quad
Externí odkaz:
http://arxiv.org/abs/2307.16197
We study the local properties of positive solutions of the equation $-\Delta u=u^p-m|\nabla u|^q$ in a punctured domain $\Omega\setminus\{0\}$ of $\mathbb{R}^N$ or in a exterior domain $\mathbb{R}^N\setminus B_{r_0}$ in the range $\min\{p,q\}>1$ and
Externí odkaz:
http://arxiv.org/abs/2303.08074
Autor:
Chen, Huyuan, Véron, Laurent
We study the isolated singularities of functions satisfying (E) (--$\Delta$) s v$\pm$|v| p--1 v = 0 in $\Omega$\{0}, v = 0 in R N \$\Omega$, where 0 < s < 1, p > 1 and $\Omega$ is a bounded domain containing the origin. We use the Caffarelli-Silvestr
Externí odkaz:
http://arxiv.org/abs/2206.04353
Publikováno v:
Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, In press
We study properties of positive functions satisfying (E) --$\Delta$u+m|$\nabla$u| q -- u p = 0 is a domain $\Omega$ or in R N + when p > 1 and 1 < q < 2. We give sufficient conditions for the existence of a solution to (E) with a nonnegative measure
Externí odkaz:
http://arxiv.org/abs/2201.09560
Autor:
Chen, Huyuan, Véron, Laurent
Publikováno v:
In Journal of Functional Analysis 1 August 2024 287(3)
We study properties of nonnegative functions satisfying (E)$\;-\Delta u+u^p-M|\nabla u|^q=0$ is a domain of $\mathbb{R}^N$ when $p>1$, $M>0$ and $1
Externí odkaz:
http://arxiv.org/abs/2107.13399
We study the existence of nonnegative solutions to the Dirichlet problem $\CL^{_{^M}}_{p,q}u:=-\Delta u+u^p-M|\nabla u|^q=\mu$ in a domain $\Omega\subset\BBR^N$ where $\mu$ is a nonnegative Radon measure, when $p>1$, $q>1$ and $M\geq 0$. We also give
Externí odkaz:
http://arxiv.org/abs/2103.02327
Autor:
Chen, Huyuan, Veron, Laurent
We provide bounds for the sequence of eigenvalues $\{\lambda_i(\Omega)\}_i$ of the Dirichlet problem $$ L_\Delta u=\lambda u\ \ {\rm in}\ \, \Omega,\quad\quad u=0\ \ {\rm in}\ \ \mathbb{R}^N\setminus \Omega,$$ where $L_\Delta$ is the logarithmic Lapl
Externí odkaz:
http://arxiv.org/abs/2011.05692
We study properties of positive functions satisfying (E) --$\Delta$u + u p -- M |$\nabla$u| q = 0 is a domain $\Omega$ or in R N + when p > 1 and 1 < q < min{p, 2}. We concentrate our research on the solutions of (E) vanishing on the boundary except
Externí odkaz:
http://arxiv.org/abs/2007.16097