Zobrazeno 1 - 10
of 233
pro vyhledávání: '"Grossi, Massimo"'
Autor:
De Regibus, Fabio, Grossi, Massimo
In this paper we prove the uniqueness of the critical point for stable solutions of the Robin problem \[ \begin{cases} -\Delta u=f(u)&\text{in }\Omega\\ u>0&\text{in }\Omega\\ \partial_\nu u+\beta u=0&\text{on }\partial\Omega, \end{cases} \] where $\
Externí odkaz:
http://arxiv.org/abs/2409.06576
Autor:
Gladiali, Francesca, Grossi, Massimo
In this paper we are concerned with the number of critical points of solutions of nonlinear elliptic equations. We will deal with the case of non-convex, contractile and non-contractile planar domains. We will prove results on the estimate of their n
Externí odkaz:
http://arxiv.org/abs/2310.04767
Autor:
Grossi, Massimo, Provenzano, Luigi
In this paper we consider semilinear equations $-\Delta u=f(u)$ with Dirichlet boundary conditions on certain convex domains of the two dimensional model spaces of constant curvature. We prove that a positive, semi-stable solution $u$ has exactly one
Externí odkaz:
http://arxiv.org/abs/2306.10641
In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem - Delta u = f(x,y) finding a geometric condition involving the curvature of the boundar
Externí odkaz:
http://arxiv.org/abs/2301.08098
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
Autor:
De Regibus, Fabio, Grossi, Massimo
In this paper we consider the second eigenfunction of the Laplacian with Dirichlet boundary conditions in convex domains. If the domain has \emph{large eccentricity} then the eigenfunction has \emph{exactly} two nondegenerate critical points (of cour
Externí odkaz:
http://arxiv.org/abs/2107.01989
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
Autor:
De Regibus, Fabio, Grossi, Massimo
In this paper we show that there exists a family of domains $\Omega_{\varepsilon}\subseteq\mathbb{R}^N$ with $N\ge2$, such that the $stable$ solution of the problem \[ \begin{cases} -\Delta u= g(u)&\hbox{in }\Omega_\varepsilon\\ u>0&\hbox{in }\Omega_
Externí odkaz:
http://arxiv.org/abs/2101.12652
In this paper we consider nodal radial solutions of the problem $$ \begin{cases} -\Delta u=|u|^{2^*-2}u+\lambda u&\text{ in }B,\\ u=0&\text{ on }\partial B \end{cases} $$ where $2^*=\frac{2N}{N-2}$ with $3\le N\le6$ and $B$ is the unit ball of $\R^N$
Externí odkaz:
http://arxiv.org/abs/2010.12311
In this paper we show the uniqueness of the critical point for \emph{semi-stable} solutions of the problem $$\begin{cases} -\Delta u=f(u)&\text{in }\Omega\\ u>0&\text{in }\Omega\\ u=0&\text{on } \partial\Omega,\end{cases}$$ where $\Omega\subset\mathb
Externí odkaz:
http://arxiv.org/abs/2004.11330