73 citations · 413 across the 37 of their papers we have counts for
47 papers
Normalized solutions to the NLS equation in the ball for any prescribed mass
Nicola Soave
Given , we consider the problem \[ \text{find such that } \begin{cases} -Δu+λu = |u|^{p-1}u & \text{in } B \\ \int_B u^2\,dx = ρ, \end{c…
On least energy solutions for a nonlinear Schrödinger system with -wise interaction
Lorenzo Giaretto, Nicola Soave
In this paper we establish existence and properties of minimal energy solutions for the weakly coupled system $$ \begin{cases} -Δu_i + λ_i u_i = μ_i|u_i|^{Kq-2}u_i + β|u_i|^{q-2}u_…
On partially segregated harmonic maps: optimal regularity and structure of the free boundary
Nicola Soave, Susanna Terracini
We consider triplets of densities minimizing the Dirichlet energy \[\sum_{j=1}^3 \int_Ω |\nabla u_j|^2\,dx \] over a bounded domain , subject…
On some singularly perturbed elliptic systems modeling partial segregation: uniform Hölder estimates and basic properties of the limits
Nicola Soave, Susanna Terracini
We prove uniform Hölder estimates in a class of singularly perturbed competition-diffusion elliptic systems, with the particular feature that the interactions between the component…
Notes on Overdetermined Singular Problems
Francesco Esposito, Berardino Sciunzi, Nicola Soave
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
A fractional Hopf Lemma for sign-changing solutions
Serena Dipierro, Nicola Soave, Enrico Valdinoci
In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differen…
The Lane-Emden system on Cartan-Hadamard manifolds: asymptotics and rigidity of radial solutions
Matteo Muratori, Nicola Soave
We investigate existence and qualitative properties of globally defined and positive radial solutions of the Lane-Emden system, posed on a Cartan-Hadamard model manifold $ \mathbb{…
Normalized solutions of -supercritical NLS equations on noncompact metric graphs with localized nonlinearities
Jack Borthwick, Xiaojun Chang, Louis Jeanjean +1
In this paper we are concerned with the existence of normalized solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities. In a -…
Bounded Palais-Smale sequences with Morse type information for some constrained functionals
Jack Borthwick, Xiaojun Chang, Louis Jeanjean +1
In this paper, we study, for functionals having a mountain pass geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information.
On the nodal set of solutions to some sublinear equations without homogeneity
Nicola Soave, Giorgio Tortone
We investigate the structure of the nodal set of solutions to an unstable Alt-Phillips type problem \[ -Δu = λ_+(u^+)^{p-1}-λ_-(u^-)^{q-1} \] where , , $λ_- \g…
Normalized solutions of -supercritical NLS equations on compact metric graphs
Xiaojun Chang, Louis Jeanjean, Nicola Soave
This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schrödinger equation on compact metric graphs. The invest…
Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius
Nicola Soave, Hugo Tavares, Alessandro Zilio
Consider the class of optimal partition problems with long range interactions \[ \inf \left\{ \sum_{i=1}^k λ_1(ω_i):\ (ω_1,\ldots, ω_k) \in \mathcal{P}_r(Ω) \right\}, \] where $λ_1…
Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds
Matteo Muratori, Nicola Soave
The Cartan-Hadamard conjecture states that, on every -dimensional Cartan-Hadamard manifold , the isoperimetric inequality holds with Euclidean optimal constant,…
Ground states for the NLS equation with combined nonlinearities on non-compact metric graphs
Dario Pierotti, Nicola Soave
We investigate the existence of ground states with prescribed mass for the NLS energy with combined -critical and subcritical nonlinearities, on a general non-compact metric g…
An anisotropic monotoncity formula, with applications to some segregation problems
Nicola Soave, Susanna Terracini
We prove an Alt-Caffarelli-Friedman montonicity formula for pairs of functions solving elliptic equations driven by different ellipticity matrices in their positivity sets. As appl…
Saddle-shaped positive solutions for elliptic systems with bistable nonlinearity
Nicola Soave
In this paper we prove the existence of infinitely many saddle-shaped positive solutions for non-cooperative nonlinear elliptic systems with bistable nonlinearities in the phase-se…
Local minimizers in absence of ground states for the critical NLS energy on metric graphs
Dario Pierotti, Nicola Soave, Gianmaria Verzini
We consider the mass-critical nonlinear Schrödinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to g…
On unique continuation principles for some elliptic systems
Ederson Moreira dos Santos, Gabrielle Nornberg, Nicola Soave
In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application,…
Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case
Nicola Soave
We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities \[ -Δu= λu + μ|u|^{q-2} u + |u|^{2^*-2} u \qquad \text{…
A fountain of positive Bubbles on a Coron's Problem for a Competitive Weakly Coupled Gradient System
Angela Pistoia, Nicola Soave, Hugo Tavares
We consider the following critical elliptic system: \begin{equation*} \begin{cases} -Δu_i=μ_i u_i^{3}+βu_i^{ } \sum\limits_{j\neq i} u_j^{2} \quad \hbox{in}\ Ω_\varepsilon \\ u_i=0…
Normalized ground states for the NLS equation with combined nonlinearities
Nicola Soave
We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities \[ -Δu= λu + μ|u|^{q-2} u + |u|^{p-2} u \qquad \text{in…
The nodal set of solutions to some elliptic problems: singular nonlinearities
Nicola Soave, Susanna Terracini
This paper deals with solutions to the equation \begin{equation*} -Δu = λ_+ \left(u^+\right)^{q-1} - λ_- \left(u^-\right)^{q-1} \quad \text{in } \end{equation*} where $λ_+,λ_-…
The nodal set of solutions to some elliptic problems: sublinear equations, and unstable two-phase membrane problem
Nicola Soave, Susanna Terracini
We are concerned with the nodal set of solutions to equations of the form \begin{equation*} -Δu = λ_+ \left(u^+\right)^{q-1} - λ_- \left(u^-\right)^{q-1} \quad \text{in } \end…
The unique continuation property of sublinear equations
Nicola Soave, Tobias Weth
We derive the unique continuation property of a class of semi-linear elliptic equations with non-Lipschitz nonlinearities. The simplest type of equations to which our results apply…