Luigi Appolloni

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20202025

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6 papers · 1 filter

math.AP2025

Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains

Luigi Appolloni, Riccardo Molle

We consider the problem $- Δ u + λ u = u^{p - 1}$ , where $u \in H_{0}^{1} (Ω)$ verifies $∥ u ∥_{L^{2}} = m > 0$ , and $λ \in [0, + \infty)$ . Here, $R^{N} ∖ Ω$ is nonempty and compact. We prove…

math.AP2025

A Note on Moving Frames along Sobolev Maps and the Regularity of Weakly Harmonic Maps

Luigi Appolloni, Ben Sharp

The purpose of this note is twofold. First we show that, for weakly differentiable maps between Riemannian manifolds of any dimension, a smallness condition on a Morrey-norm of the…

math.AP2022

Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities

Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi

We study the equation $- Δ_{g} w + w = λ α (σ) f (w)$ on a $d$ -dimensional homogeneous Cartan-Hadamard Manifold $M$ with $d \geq 3$ . Without using the theory of topological indices…

math.AP2022

Multiple solutions for Schrödinger equations on Riemannian manifolds via $\nabla$ -theorems

Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi

We consider a smooth, complete and non-compact Riemannian manifold $(M, g)$ of dimension $d \geq 3$ , and we look for positive solutions to the semilinear elliptic equation…

math.AP2021

On Critical Kirchhoff problems driven by the fractional Laplacian

Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi

We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the sens…

math.AP2020

Normalized solutions for the fractional NLS with mass supercritical nonlinearity

Luigi Appolloni, Simone Secchi

We investigate the existence of solutions to the fractional nonlinear Schrödinger equation $(- Δ)^{s} u = f (u)$ with prescribed $L^{2}$ -norm $\int_{R^{N}} ∣ u ∣^{2} d x = m$ in the…

Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains

A Note on Moving Frames along Sobolev Maps and the Regularity of Weakly Harmonic Maps

Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities

Multiple solutions for Schrödinger equations on Riemannian manifolds via ∇-theorems

On Critical Kirchhoff problems driven by the fractional Laplacian

Normalized solutions for the fractional NLS with mass supercritical nonlinearity

Multiple solutions for Schrödinger equations on Riemannian manifolds via $\nabla$ -theorems