-
Article
Classification of radial blow-up at the first critical exponent for the Lin–Ni–Takagi problem in the ball
We investigate the behaviour of radial solutions to the Lin–Ni–Takagi problem in the ball \(B_R \subset \mathbb {R}^N\) ...
-
Article
A Sharp Gradient Estimate and \(W^{2,q}\) Regularity for the Prescribed Mean Curvature Equation in the Lorentz-Minkowski Space
We consider the prescribed mean curvature equation for entire spacelike hypersurfaces in the Lorentz-Minkowski space, namely $$\begin{aligned}...
-
Article
Unbounded mass radial solutions for the Keller–Segel equation in the disk
We consider the boundary value problem $$\begin{aligned}\left\{ \begin{array}{rcll} -\Delta u+ u -\lambda e^u&{}=&{}0,\ u>0 &{} \mathrm {in}\ ...
-
Article
Symmetry Results in Two-Dimensional Inequalities for Aharonov–Bohm Magnetic Fields
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrödinger operator involving an Aharonov–Bohm magnetic vector potential. We investigate the symmetry prope...
-
Article
On the Born–Infeld equation for electrostatic fields with a superposition of point charges
In this paper, we study the static Born–Infeld equation $$\begin{aligned} -\mathrm {div}\left( \frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\...
-
Article
On the Regularity of the Minimizer of the Electrostatic Born–Infeld Energy
We consider the electrostatic Born–Infeld energy $$\int_{\mathbb{R}^N}\left(1-{\sqrt{1-|\nabla u|^2}}\right)\, {\rm d}x -\int_{\mathbb...
-
Article
Multiple positive solutions of the stationary Keller–Segel system
We consider the stationary Keller–Segel equation $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta v+v=\lambda e^v, \quad v>0 \quad...
-
Article
Layered solutions with unbounded mass for the Keller–Segel equation
In this paper, we construct several families of radial solutions for the stationary Keller–Segel equation. The first one consists in solutions which concentrate simultaneously on the interior and on the exteri...
-
Article
One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in ℝ N
In this paper, the authors prove an analogue of Gibbons’ conjecture for the extended fourth order Allen-Cahn equation in ℝ N , as well as Liouville type results for some solution...
-
Article
Heteroclinic solutions of singular quasilinear bistable equations
In this note we consider the action functional $$\begin{aligned} \int _{\mathbb {R}\times \omega } \left( 1 - \sqrt{1 - |\nabla u|^{2}} + W(u)...
-
Article
The limit as \(p\rightarrow \infty \) in the eigenvalue problem for a system of p-Laplacians
In this paper, we study the behavior as \(p\rightarrow \infty \) ...
-
Article
On the Electrostatic Born–Infeld Equation with Extended Charges
In this paper, we deal with the electrostatic Born–Infeld equation $$\left\{\begin{array}{ll}-\operatorname{div} \left(\displaystyle\f...
-
Article
Nonlinear Schrödinger equation: concentration on circles driven by an external magnetic field
In this paper, we study the semiclassical limit for the stationary magnetic nonlinear Schrödinger equation $$\begin{aligned} \left( i ...
-
Article
Qualitative properties of solutions to mixed-diffusion bistable equations
We consider a fourth-order extension of the Allen–Cahn model with mixed-diffusion and Navier boundary conditions. Using variational and bifurcation methods, we prove results on existence, uniqueness, positivit...
-
Chapter
Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion
In this note we provide some simple results for the 4NLS model i ...
-
Article
Multiple positive radial solutions on annuli for nonlinear Neumann problems with large growth
We consider a classical semilinear elliptic equation with Neumann boundary conditions on an annulus in R N . The nonlinear term is the product of a radially symm...
-
Article
Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity
Groundstates of the stationary nonlinear Schrödinger equation $$-\Delta u +V u =K u^{p-1}$$ , are studied when the non...
-
Article
Littlewood’s problem for isochronous oscillators
We study the boundedness problem for a class of forced isochronous oscillators.
-
Article
On the Petrials of thin rank 3 geometries
The aim of this paper is to extend the concept of a Petrial to thin (regular) rank three geometries. The main result is that if the Petrial of a thin regular residually connected geometry Γ is also a thin geo...
