107 citations · 382 across the 27 of their papers we have counts for
4 papers · 1 filter
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with equations
Simão Correia, Filipe Oliveira, Hugo Tavares
In this work we consider the weakly coupled Schrödinger cubic system \[ \begin{cases} \displaystyle -Δu_i+λ_i u_i= μ_i u_i^{3}+ u_i\sum_{j\neq i}b_{ij} u_j^2 \\ u_i\in H^1(\mathbb{…
Dividing the circle
Pedro J. Freitas, Hugo Tavares
There are known constructions for some regular polygons, usually inscribed in a circle, but not for all polygons - the Gauss-Wantzel Theorem states precisely which ones can be cons…
Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping
Nicola Soave, Hugo Tavares, Susanna Terracini +1
We study regularity issues for systems of elliptic equations of the type \[ -Δu_i=f_{i,β}(x)-β\sum_{j\neq i} a_{ij} u_i |u_i|^{p-1}|u_j|^{p+1} \] set in domains $Ω\subset \mathbb{R…
Ground States for a nonlinear Schrödinger system with sublinear coupling terms
Filipe Oliveira, Hugo Tavares
We study the existence of ground states for the coupled Schrödinger system \begin{equation} \left\{\begin{array}{lll} \displaystyle -Δu_i+λ_i u_i= μ_i |u_i|^{2q-2}u_i+\sum_{j\neq i…