10 papers
Nondegeneracy of low-energy nodal solutions to the Yamabe equation
Sérgio L. N. Neves, Angela Pistoia
We study the linearized Yamabe equation in , or equivalently on $\s^n$, at a low-energy sign-changing solution with two nodal domains. We consider odd dimensions and…
A fractional critical problem in the halfspace with Neumann conditions
Azahara DelaTorre, Azahara DelaTorre Pedraza, Serena Dipierro +2
Given and , we construct nontrivial solutions of the problem \begin{equation*} \begin{cases} (-Δ)^s u=u^{2^*_s-1} &{\mbox{ in }}\mathbb{R}^n_+,\\ {\mathcal{N}}_s…
Sign-changing multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions
Angela Pistoia, Giuseppe Mario Rago, Giusi Vaira
We construct families of sign-changing solutions for the four-dimensional Brezis--Nirenberg problem \[ -Δu=u^3+\varepsilon u\quad\text{in }Ω,\qquad u=0\quad\text{on }\partialΩ, \]…
Sign-changing solutions to the Yamabe problem on a spherical cap
Mónica Clapp, Benedetta Pellacci, Angela Pistoia
Spherical caps play a crucial role in establishing a criterion for the existence of solutions to the Yamabe problem on a compact Riemannian manifold with boundary, similar to the r…
Blowing-up solutions to a critical 4D Neumann system in a competitive regime
Qing Guo, Angela Pistoia, Shixin Wen
We build blowing-up solutions to the critical elliptic system with Neumann boundary condition, \begin{equation*} \begin{cases} -Δu_1 + λu_1 = u_1^{3} -βu_1u_2^2 & \text{in } Ω, -Δu…
Entire solutions to a strongly competitive nonlinear Schrödinger system
Pierpaolo Esposito, Pablo Figueroa, Angela Pistoia +1
We build infinitely-many non-radial positive solutions to the Schrödinger system \begin{equation*} \left\{\begin{aligned} &-Δu_1+u_1=u_1^{{\mathfrak p} }-Λu_1^{a_1} u_2^{a_2}\ \hbo…
Sign-changing solutions for critical Hamiltonian systems in
Yuxia Guo, Seunghyeok Kim, Angela Pistoia +1
We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$ -Δu =|v|^{p-1}v\ \hbox{in}\ \mathbb{R}^N,\ -Δv =|u|^…
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=…
Existence and multiplicity of peaked bound states for nonlinear Schrödinger equations on metric graphs
Haixia Chen, Simone Dovetta, Angela Pistoia +1
We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schrödinger equations on general compact and noncompact metric graphs. Pr…
Blow-up for sign-changing solutions of the critical heat equation in domains with a small hole
I. Ianni, M. Musso, A. Pistoia
We consider the critical heat equation \begin{equation} \label{CH}\tag{CH} \begin{array}{lr} v_t-Δv =|v|^{\frac{4}{n-2}}v & Ω_ε\times (0, +\infty) \\ v=0 & \partialΩ_ε\times (0, +\…