73 citations · 413 across the 37 of their papers we have counts for
5 papers · 1 filter
New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation terms
Nicola Soave, Hugo Tavares
In this paper we focus on existence and symmetry properties of solutions to the cubic Schrödinger system \[ -Δu_i +λ_i u_i = \sum_{j=1}^d β_{ij} u_j^2 u_i \quad \text{in $Ω\subset…
Overdetermined problems for the fractional Laplacian in exterior and annular sets
Nicola Soave, Enrico Valdinoci
We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are…
Uniform bounds for strongly competing systems: the optimal Lipschitz case
Nicola Soave, Alessandro Zilio
For a class of systems of semi-linear elliptic equations, including \[ -Δu_i=f_i(x,u_i) - βu_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for (variational-type interacti…
Avoiding collisions under topological constraints in variational problems coming from celestial mechanics
Nicola Soave, Susanna Terracini
In a singular potential setting, we generalize a method which allows to show that minimizers under topological constraints of the action functional (or of the Maupertuis') are coll…
Liouville theorems and -dimensional symmetry for solutions of an elliptic system modelling phase separation
Nicola Soave, Susanna Terracini
We consider solutions of the competitive elliptic system \[ \left\{ \begin{array}{ll} -Δu_i = - \sum_{j \neq i} u_i u_j^2 & \text{in } \\ u_i >0 & \text{in $\mathbb{R…