6 papers · 1 filter
The Allen-Cahn equation and general minimal cones
Oscar Ivan Agudelo Rico, Matteo Rizzi
We construct solutions to the Allen-Cahn equation in , with , whose zero level set is asymptotic (at infinity) to a given minimal cone. Our c…
Global boundedness and normalized solutions to a -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|^…
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{…
Normalised solutions for -Laplacian equations with -supercritical growth
Raj Narayan Dhara, Matteo Rizzi
For and , 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 }\\ \|u\|_2&=ρ\end{align*…
Normalized solutions of mass supercritical Schrodinger-Poisson equation with potential
Xueqin Peng, Matteo Rizzi
In this paper we prove the existence of normalized solutions to the following Schrödinger-Poisson equation $$ \begin{cases} -Δu+V(…
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…