Giusi Vaira

activity

20092022

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11 papers · 1 filter

math.AP2020

Nodal solutions of the Brezis-Nirenberg problem in dimension 6

Angela Pistoia, Giusi Vaira

We show that the classical Brezis-Nirenberg problem $- Δ u = u ∣ u ∣ + λ u in Ω, u = 0 on \partial Ω,$ when $Ω$ is a bounded domain in $R^{6}$ has a sign-changing…

math.AP2019

Normalized concentrating solutions to nonlinear elliptic problems

Benedetta Pellacci, Angela Pistoia, Giusi Vaira +1

We prove the existence of solutions $(λ, v) \in R \times H^{1} (Ω)$ of the elliptic problem \[ \begin{cases} -Δv+(V(x)+λ) v =v^{p}\ &\text{ in $Ω,$ } \ v>0,\qquad \int_Ωv^2\…

math.AP2019

Nondegeneracy of the bubble for the critical p-Laplace equation

Angela Pistoia, Giusi Vaira

We prove the non-degeneracy of the extremals of the Sobolev inequality $$\int\limits_{\mathbb R^N}|\nabla u|^pdx\ge \mathcal S_p\int\limits_{\mathbb R^N}|u|^{Np\over N-p}dx,\ u\in…

math.AP2018

Radial symmetry for a quasilinear elliptic equation with a critical Sobolev growth and Hardy potential

Francescantonio Oliva, Berardino Sciunzi, Giusi Vaira

We consider weak positive solutions to the critical $p$ -Laplace equation with Hardy potential in $R^{N}$ $- Δ_{p} u - \frac{γ}{∣ x ∣ ^{p}} u^{p - 1} = u^{p^{*} - 1}$ where $1 < p < N$ , $0\le γ<\l…

math.AP2018

Maximal solution of the Liouville equation in doubly connected domains

Michal Kowalczyk, Angela Pistoia, Giusi Vaira

In this paper we consider the Liouville equation $Δ u + λ^{2} e^{u} = 0$ with Dirichlet boundary conditions in a two dimensional, doubly connected domain $Ω$ . We show that there exists…

math.AP2018

Free boundary problems arising in the theory of maximal solutions of equations with exponential nonlinearities

Michal Kowalczyk, Angela Pistoia, Piotr Rybka +1

We consider equations of the form $Δ u + λ^{2} V (x) e^{u} = ρ$ in various two dimensional settings. We assume that $V > 0$ is a given function, $λ > 0$ is a small parameter and $ρ=\mathcal…