5 papers
Multiple solutions and simulations for an Ion Flow Field problem applied to HVDC transmission lines
Madeline Chauvier, Serge Nicaise, Christophe Troestler +1
This paper initiates a mathematical investigation of a PDE model for the transport of high voltage direct current via overhead lines. We prove the existence of infinitely many solu…
Blow-up analysis and a priori bounds for NLS equations on metric graphs
Pablo Carrillo, Colette De Coster, Damien Galant +2
We consider, on a connected metric graph , a family of nonlinear Schrödinger equations $$ -u'' + W_n(x) u + λ_n u = Ï_n(x)|u|^{p-2}u, \quad n \in \mathbb{N}. \qquad…
Normalized vector solutions of nonlinear Schrödinger systems
Xiaomeng Huang, Angela Pistoia, Christophe Troestler +1
Given we look for solutions and of the system \[ \begin{cases} \displaystyle -Îv_i+ λv_i+V_i(x)v_i = \sum_{\substac…
Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems
Guglielmo Feltrin, Christophe Troestler
In this paper, we focus our attention on the positive solutions to second-order nonlinear ordinary differential equations of the form , where is a sign-changing…
Infinitely many normalized solutions of -supercritical NLS equations on noncompact metric graphs with localized nonlinearities
Pablo Carrillo, Damien Galant, Louis Jeanjean +1
We consider the existence of solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities. In an -supercritical regime, we establis…