7 citations · 13 across the 12 of their papers we have counts for
16 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 = ρ_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 -Δv_i+ λv_i+V_i(x)v_i = \sum_{\substack{j=…
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 establish…
Constant sign and sign changing NLS ground states on noncompact metric graphs
Colette De Coster, Simone Dovetta, Damien Galant +2
We investigate existence and nonexistence of action ground states and nodal action ground states for the nonlinear Schrödinger equation on noncompact metric graphs with rather gene…
A computer assisted proof of the symmetries of least energy nodal solutions on squares
Ariel Salort, Christophe Troestler
In this article, we prove that the least energy nodal solutions to Lane-Emden equation with zero Dirichlet boundary conditions on a square are odd with respect t…
Entire radial and nonradial solutions for systems with critical growth
Francesca Gladiali, Massimo Grossi, Christophe Troestler
In this paper we establish existence of radial and nonradial solutions to the system $$ \begin{array}{ll} -Δu_1 = F_1(u_1,u_2) &\text{in }\mathbb{R}^N,\newline -Δu_2 = F_2(u_1,u_2)…
Spectral analysis of a generalized buckling problem on a ball
Colette De Coster, Serge Nicaise, Christophe Troestler
In this paper, the spectrum of the following fourth order problem \begin{equation*} \begin{cases} Δ^2 u+νu=-λΔu &\text{in } D_1,\newline u=\partial_r u= 0 &\text{on } \partial D_1,…
A non-variational system involving the critical Sobolev exponent. The radial case
Francesca Gladiali, Massimo Grossi, Christophe Troestler
In this paper we consider the non-variational system $$ \begin{cases} -Δu_i = \sum\limits_{j=1}^k a_{ij} u_j^{(N+2)/(N-2)} &\text{in }\mathbb R^N,\newline u_i>0 &\text{in }\mathbb…
Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions
Denis Bonheure, Christopher Grumiau, Christophe Troestler
Assuming is a ball in , we analyze the positive solutions of the problem \[ \begin{cases} -Δu+u= |u|^{p-2}u, &\text{ in } B_{R},\newline \partial_νu=0,&\text…
Nodal properties of eigenfunctions of a generalized buckling problem on balls
Colette De Coster, Serge Nicaise, Christophe Troestler
In this paper we are interested in the following fourth order eigenvalue problem coming from the buckling of thin films on liquid substrates: \begin{equation*} \begin{cases} Δ^2 u+…
Asymptotic symmetries for fractional operators
C. Grumiau, M. Squassina, C. Troestler
In this paper, we study equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. More precisely, we study the pr…
Convergence of a mountain pass type algorithm for strongly indefinite problems and systems
Christopher Grumiau, Christophe Troestler
For a functional $\E$ and a peak selection that picks up a global maximum of $\E$ on varying cones, we study the convergence up to a subsequence to a critical point of the sequence…
Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potential
Christophe Troestler
This paper shows that the nonlinear periodic eigenvalue problem $${cases} -Δu + V(x) u - f(x,u) = λu, u \in H^1(\IR^N), {cases}$$ has a nontrivial branch of solutions emanating fro…
On the Mountain-pass algorithm for the quasi-linear Schrodinger equation
Christopher Grumiau, Marco Squassina, Christophe Troestler
We discuss the application of the Mountain Pass algorithm to the so-called quasi-linear Schrodinger equation, which is naturally associated with a class of nonsmooth functionals so…