Nicola Soave

On existence and phase separation of solitary waves for nonlinear Schrödinger systems modelling simultaneous cooperation and competition

We study existence and phase separation, and the relation between these two aspects, of positive bound states for the nonlinear elliptic system

Bounded solutions for a forced bounded oscillator without friction

\begin{aligned} \left\{ \begin{array}{l@{\quad }l} - \Delta u_i + \lambda _i u_i = \sum \nolimits _{j=1}^d \beta _{ij} u_j^2 u_i &{} \hbox { in }\, \Omega \\ u_1 =\cdots = u_d=0 &{} \hbox { on }\, \partial \Omega . \end{array}\right. \end{aligned}

The Unique Continuation Property of Sublinear Equations

-Δui+λiui=∑j=1dβijuj2uiinΩu1=⋯=ud=0on∂Ω.This system arises when searching for solitary waves for the Gross–Pitaevskii equations. We focus on the case of simultaneous cooperation and competition, that is, we assume that there exist two pairs

Monotonicity and 1-Dimensional Symmetry for Solutions of an Elliptic System Arising in Bose-Einstein Condensation

(i_1,j_1)

N

(i1,j1) and