22 citations · 42 across the 13 of their papers we have counts for
15 papers
Higher-order criteria and sharpness for blow-up at quantized singularities in Liouville equations
Teresa D'Aprile, Juncheng Wei, Lei Zhang
This work is devoted to the study of blow-up phenomena for solutions of \[-Δu=λV(x)|x|^{2N}e^v,\quad \mbox{in}\quad B_1,\quad v=0\quad \mbox{on}\quad \partial B_1. \] where d…
Second order classification for singular Liouville equations with a coefficient function
Teresa D'Aprile, Juncheng Wei, Lei Zhang
In this article we are concerned with the existence of blow-up solutions to the following boundary value problem $$-Δv= λV(x) |x|^2e^v\;\mbox{in}\quad B_1,\quad v=0 \;\mbox{ on }\q…
High Order Vanishing Theorems for Nonsimple Blowup Solutions of Singular Liouville Equation
Teresa D'Aprile, Juncheng Wei, Lei Zhang
For a singular Liouville equation, it is plausible that a non-simple blowup phenomenon occurs around a quantized singular pole. The presence of complex blowup profiles of bubbling…
On the construction of non-simple blow-up solutions for the singular Liouville equation with a potential
Teresa D'Aprile, Juncheng Wei, Lei Zhang
We are concerned with the existence of blowing-up solutions to the following boundary value problem $$-Δu= λV(x) e^u-4πN δ_0\;\mbox{ in } B_1,\quad u=0 \;\mbox{ on }\partial B_1,$$…
On Non-simple blowup solutions of Liouville equation
Teresa D'Aprile, Juncheng Wei, Lei Zhang
For Liouville equation with quantized singular sources, the non-simple blowup phenomenon has been a major difficulty for years. It was conjectured by the first two authors that the…
Blow-up phenomena for the Liouville equation with a singular source of integer multiplicity
Teresa D'Aprile
We are concerned with the existence of blowing-up solutions to the following boundary value problem $$-Δu= \la a(x) e^u-4πN δ_0\;\hbox{ in } Ω,\quad u=0 \;\hbox{ on }\partial Ω,$$…
Prescribed Gauss curvature problem on singular surfaces
Teresa D'Aprile, Francesca De Marchis, Isabella Ianni
We study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface admitting conical singularities of orders 's at points 's…
Equilibria of point-vortices on closed surfaces
Teresa D'Aprile, Pierpaolo Esposito
We discuss the existence of equilibrium configurations for the Hamiltonian point-vortex model on a closed surface . The topological properties of determine the occurrence of…
Asymmetric blow-up for the SU(3) Toda System
Teresa D'Aprile, Angela Pistoia, David Ruiz
We consider the so-called Toda system in a smooth planar domain under homogeneous Dirichlet boundary conditions. We prove the existence of a continuum of solutions for which both c…
A continuum of solutions for the SU(3) Toda System exhibiting partial blow-up
Teresa D'Aprile, Angela Pistoia, David Ruiz
In this paper we consider the so-called Toda System in planar domains under Dirichlet boundary condition. We show the existence of continua of solutions for which one component is…
Solutions with multiple alternate sign peaks along a boundary geodesic to a semilinear Dirichlet problem
Teresa D'Aprile, Angela Pistoia
We study the existence of sign-changing multiple interior spike solutions for the following Dirichlet problem {equation*}\e^2Δv-v+f(v)=0\hbox{in}Ω,\quad v=0 \hbox{on}\partial Ω,{eq…
Multiple blow-up solutions for the Liouville equation with singular data
Teresa D'Aprile
We study the existence of solutions with multiple concentration to the following boundary value problem $$-Δu=\e^2 e^u-4π\sum_{p\in Z}α_p δ_{p}\;\hbox{in} Ω,\quad u=0 \;\hbox{on}\p…
On the profile of sign changing solutions of an almost critical problem in the ball
Thomas Bartsch, Teresa D'Aprile, Angela Pistoia
We study the existence and the profile of sign-changing solutions to the slightly subcritical problem $$ -\De u=|u|^{2^*-2-\eps}u \hbox{in} \cB, \quad u=0 \hbox{on}\partial \cB, $$…
Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries
Thomas Bartsch, Teresa D'Aprile, Angela Pistoia
We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem $$-Δu=|u|^{2^*-2-\e}u \hbox{in}Ω, \quad u=0 \hbox{on}\partial Ω,$$ where…
Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems
Teresa D'Aprile, David Ruiz
We study the existence of positive and sign-changing multipeak solutions for the stationary Nonlinear Schroedinger Equation. Here no symmetry on is assumed. It is known that th…