Matteo Rizzi

activity

20232026

collaborators

6 papers

math.AP2026

The Allen-Cahn equation and general minimal cones

Oscar Ivan Agudelo Rico, Matteo Rizzi

We construct solutions to the Allen-Cahn equation $Δ u + u - u^{3} = 0$ in $R^{N + 1}$ , with $N \geq 3$ , whose zero level set is asymptotic (at infinity) to a given minimal cone. Our c…

math.AP2026

Global boundedness and normalized solutions to a $p$ -Laplacian equation

Raj Narayan Dhara, Matteo Rizzi

In the paper, we prove the existence of radial solutions to \begin{equation}\notag%\label{main-eq-abstarct} %\begin{aligned} -Δ_p u+({\rm sgn}(p-s)+V(x))|u|^{p-2}u+λ|u|^{s-2}u=|u|^…

math.AP2025

Normalized solutions for the nonlinear Schrödinger equation with potentials

Matteo Rizzi, Xueqin Peng

In this paper, we find normalized solutions to the following Schrödinger equation \begin{equation}\notag \begin{aligned} &-Δu-\fracμ{|x|^2}h(x)u+λu =f(u)\quad\text{in}\quad\mathbb{…

math.AP2025

Normalised solutions for $p$ -Laplacian equations with $L^{p}$ -supercritical growth

Raj Narayan Dhara, Matteo Rizzi

For $N \geq 3$ and $2 < p < N$ , we find normalised solutions to the equation \begin{align*} -Δ_p u+(1+V(x))|u|^{p-2}u+λu&=|u|^{q-2}u\qquad\text{in $R^{N}$ }\\ \|u\|_2&=ρ\end{align*…

math.AP2023

Normalized solutions of mass supercritical Schrodinger-Poisson equation with potential

Xueqin Peng, Matteo Rizzi

In this paper we prove the existence of normalized solutions $(λ, u) \subset (0, \infty) \times H^{1} (R^{3})$ to the following Schrödinger-Poisson equation $$ \begin{cases} -Δu+V(…

math.AP2023

Some rigidity results and asymptotic porperties for solutions to semilinear elliptic P.D.E

Matteo Rizzi, Panayotis Smyrnelis

We will present some rigidity results for solutions to semilinear elliptic equations of the form $\Deltau = W'(u)$, where W is a quite general potential with a local minimum and a…