128 citations · 524 across the 29 of their papers we have counts for
36 papers
Classification of radial blow-up at the first critical exponent for the Lin-Ni-Takagi problem in the ball
Denis Bonheure, Jean-Baptiste Casteras, Bruno Premoselli
We investigate the behaviour of radial solutions to the Lin-Ni-Takagi problem in the ball for : \begin{equation*} \left \{ \begin{aligned} - \tr…
A sharp gradient estimate and regularity for the prescribed mean curvature equation in the Lorentz-Minkowski space
Denis Bonheure, Alessandro Iacopetti
We consider the prescribed mean curvature equation for entire spacelike hypersurfaces in the Lorentz-Minkowski space, namely \begin{equation*} -\operatorname{div}\left(\displaystyl…
Bifurcation analysis of the Hardy-Sobolev equation
Denis Bonheure, Jean-Baptiste Casteras, Francesca Gladiali
In this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation $$\begin{cases} -Δu-\displaystyle\frac γ{|x|^2}u=\displaystyle\frac{1}{|x|^s}|u|^{p…
Concentration phenomena for the Schrödinger-Poisson system in
Denis Bonheure, Silvia Cingolani, Simone Secchi
We perform a semiclassical analysis for the planar Schrödinger-Poisson system \[ \cases{ -\varepsilon^{2} Δψ+V(x)ψ= E(x) ψ\quad \text{in },\cr -ΔE= |ψ|^{2} \quad \tex…
Long-time dynamics of a hinged-free plate driven by a non-conservative force
Denis Bonheure, Filippo Gazzola, Irena Lasiecka +1
A partially hinged, partially free rectangular plate is considered, with the aim to address the possible unstable end behaviors of a suspension bridge subject to wind. This leads t…
Equilibrium configuration of a rectangular obstacle immersed in a channel flow
Denis Bonheure, Giovanni P. Galdi, Filippo Gazzola
Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may…
Nodal Solutions for sublinear-type problems with Dirichlet boundary conditions
Denis Bonheure, Ederson Moreira dos Santos, Enea Parini +2
We consider nonlinear second order elliptic problems of the type \[ -Δu=f(u) \text{ in } Ω, \qquad u=0 \text{ on } \partial Ω, \] where is an open -domain in $\mathbb{…
A Paneitz-Branson type equation with Neumann boundary conditions
Denis Bonheure, Hussein Cheikh Ali, Robson Nascimento
We consider the best constant in a critical Sobolev inequality of second order. We show non-rigidity for the optimizers above a certain threshold, namely we prove that the best con…
Inequalities involving Aharonov-Bohm magnetic potentials in dimensions 2 and 3
Denis Bonheure, Jean Dolbeault, Maria J. Esteban +2
This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schr{ö}dinger operators involving Aharonov-Bohm magnetic potentials, and to…
Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields
Denis Bonheure, Jean Dolbeault, Maria J. Esteban +2
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schr{ö}dinger operator involving an Aharonov-Bohm magnetic vector potential. We…
Equilibrium measures and equilibrium potentials in the Born-Infeld model
Denis Bonheure, Pietro d'Avenia, Alessio Pomponio +1
In this paper, we consider the electrostatic Born-Infeld model \begin{equation*} \tag{} \left\{ \begin{array}{rcll} -\operatorname{div}\left(\displaystyle\frac{\nabla…
Periodic solutions and torsional instability in a nonlinear nonlocal plate equation
Denis Bonheure, Filippo Gazzola, Ederson Moreira dos Santos
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation…
Singular radial solutions for the Keller-Segel equation in high dimension
Denis Bonheure, Jean-Baptiste Casteras, Juraj Foldes
We study singular radially symmetric solution of the stationary Keller-Segel equation, that is, an elliptic equation with exponential nonlinearity, which is super-critical in dimen…
On the regularity of the minimizer of the electrostatic Born-Infeld energy
Denis Bonheure, Alessandro Iacopetti
We consider the electrostatic Born-Infeld energy \begin{equation*} \int_{\mathbb{R}^N}\left(1-{\sqrt{1-|\nabla u|^2}}\right)\, dx -\int_{\mathbb{R}^N}ρu\, dx, \end{equation*} where…
On a fourth order nonlinear Helmholtz equation
Denis Bonheure, Jean-Baptiste Casteras, Rainer Mandel
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation in for positive, bounded and -peri…
Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation under the constr…
Spacelike radial graphs of prescribed mean curvature in the Lorentz-Minkowski space
Denis Bonheure, Alessandro Iacopetti
In this paper we investigate the existence and uniqueness of spacelike radial graphs of prescribed mean curvature in the Lorentz-Minkowski space , for ,…
Orbitally stable standing waves of a mixed dispersion nonlinear Schrödinger equation
Denis Bonheure, Jean-Baptiste Castéras, Ederson Moreira dos Santos +1
We study the mixed dispersion fourth order nonlinear Schrödinger equation \begin{equation*} %\tag{\protect{4NLS}}\label{4nls} i \partial_t ψ-γΔ^2 ψ+βΔψ+|ψ|^{2σ} ψ=0\ \text{in}\ \R…
Unbounded mass radial solutions for the Keller-Segel equation in the disk
Denis Bonheure, Jean-Baptiste Casteras, Carlos Román
We consider the boundary value problem $$ \left\{ \begin{array}{rcll} -Δu+ u -λe^u&=&0,\ u>0 & \mathrm{in}\ B_1(0)\\ \partial_νu&=&0&\mathrm{on}\ \partial B_1(0), \end{array}\right…
On the Born-Infeld equation for electrostatic fields with a superposition of point charges
Denis Bonheure, Francesca Colasuonno, Juraj Foldes
In this paper, we study the static Born-Infeld equation $$ -\mathrm{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)=\sum_{k=1}^n a_kδ_{x_k}\quad\mbox{in }\mathbb R^N,\qquad…
Strong instability of ground states to a fourth order Schrödinger equation
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr\" odinger equations. This extends the first rigorous results on blow…
The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate
Denis Bonheure, Silvia Cingolani, Jean Van Schaftingen
We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation $$ - Δu + a u = \frac{1}{2 π} \Bigl[\ln \frac{1}{|x|}* |u|^2…
Paths to uniqueness of critical points and applications to partial differential equations
Denis Bonheure, Juraj Földes, Ederson Moreira dos Santos +2
We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our me…
Properties of groundstates of nonlinear Schrödinger equations under a weak constant magnetic field
Denis Bonheure, Manon Nys, Jean Van Schaftingen
We study the qualitative properties of groundstates of the time-independent magnetic semilinear Schrödinger equation \[ - (\nabla + i A)^2 u + u = |u|^{p-2} u, \qquad \text{ in } \…