R. Molle

activity

20132026

most citedNormalized positive solutions for Schrödinger equations with potentials in unbounded domains

9 citations · 20 across the 18 of their papers we have counts for

collaborators

21 papers

math.AP2026

Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations

Xiaoming An, Lun Guo, Xiao Luo +1

We prove the uniqueness, asymptotics, symmetry, and orbital stability of energy ground states for 3D magnetic Gross-Pitaevskii equations under mild conditions on the electric poten…

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.AP2023

Positive solutions to nonlinear elliptic problems involving Sobolev exponent

Carlo Mercuri, Riccardo Molle

In this paper we consider nonlinear elliptic PDEs of the type $$-Δ_p u+a(x)|u|^{p-2}u=|u|^{p^*-2}u \qquad \mbox{ in }Ω,$$ where $1 < p < N$ and $p^{*} = N p / (N - p)$ is the critical Sobolev e…

math.AP2023

Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation

Riccardo Molle, Vitaly Moroz, Giuseppe Riey

We study normalised solutions of the stationary Gross-Pitaevskii-Poisson (GPP) equation with a defocusing local nonlinear term, $$-Δu+λu+|u|^2u =(I_α*|u|^2)u\quad\text{in $\mathbb…

math.AP2022

Standing waves for two-component elliptic system with critical growth in $R^{4}$ : the attractive case

Lun Guo, Qi Li, Xiao Luo +1

In this paper, we consider the following two-component elliptic system with critical growth \begin{equation*} \begin{cases} -Δu+(V_1(x)+λ)u=μ_1u^{3}+βuv^{2}, \ \ x\in \mathbb{R}^4,…

math.AP2022★ 9 cited

Normalized positive solutions for Schrödinger equations with potentials in unbounded domains

Sergio Lancelotti, Riccardo Molle

The paper deals with the existence of positive solutions with prescribed $L^{2}$ norm for the Schrödinger equation $$ -Δu+λu+V(x)u=|u|^{p-2}u,\qquad u\in H^1_0(Ω),\quad\int_Ωu^2dx=ρ^…

math.AP2022

On a planar Schrödinger-Poisson system involving a non-symmetric potential

Riccardo Molle, Andrea Sardilli

We prove the existence of a ground state positive solution of Schrödinger-Poisson systems in the plane of the form $$ -Δu + V(x)u + \fracγ{2π} \left(\log|\cdot| \ast u^2 \right)u =…

math.AP2022★ 3 cited

Variational properties of the first curve of the Fuč\'ık spectrum for elliptic operators

Riccardo Molle, Donato Passaseo

In this paper we present a new variational characteriztion of the first nontrival curve of the Fuč\'ık spectrum for elliptic operators with Dirichlet boundary conditions. Moreover,…

math.AP2021

Infinitely many solutions for elliptic equations with non-symmetric nonlinearities

Riccardo Molle, Donato Passaeo

We deal with the existence of infinitely many solutions for a class of elliptic problems with non-symmetric nonlinearities. Our result, which is motivated by a well known conjectur…

math.AP2021

Normalized solutions to mass supercritical Schrodinger equations with negative potential

Riccardo Molle, Giuseppe Riey, Gianmaria Verzini

We study the existence of positive solutions with prescribed $L^{2}$ -norm for the Schrödinger equation \[ -Δu-V(x)u+λu=|u|^{p-2}u\qquadλ\in \mathbb{R},\quad u\in H^1(\mathbb{R}^N), \…

math.AP2020

Normalized solutions of mass supercritical Schrödinger equations with potential

Thomas Bartsch, Riccardo Molle, Matteo Rizzi +1

This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation \[ -Δu+V(x)u+λu = |u|^{p-2}u \qquad\text{in $R^{N}$ } \] in the mass…

math.AP2019★ 6 cited

Infinitely many positive solutions of nonlinear Schrodinger equations

Riccardo Molle, Donato Passaseo

The paper deals with the equation $- Δ u + a (x) u = ∣ u ∣^{p - 1} u$ , $u \in H^{1} (R^{N})$ , with $N \geq 2$ , $p > 1, p < \frac{N + 2}{N - 2}$ if $N \geq 3$ , $a \in L_{l oc}^{N /2} (R^{N})$ , $\i…

math.AP2019★ 1 cited

Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth

Riccardo Molle, Donato Passaseo

We are concerned with Dirichlet problems of the form $${\mathop{\rm div}\nolimits} (|D u|^{p-2}Du)+f(u)=0\ \mbox{ in }Ω,\qquad u=0\ \mbox{ on }\partialΩ, $$ where $Ω$ is a bounded…

math.AP2019

Nonexistence of solutions for Dirichlet problems with supercritical growth in tubular domains

Riccardo Molle, Donato Passaseo

We deal with Dirichlet problems of the form $$ Δu+f(u)=0 \mbox{ in }Ω,\qquad u=0\ \mbox{ on }\partial Ω$$ where $Ω$ is a bounded domain of $R^{n}$ , $n \geq 3$ , and $f$ has sup…

math.AP2019

Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains

Riccardo Molle, Donato Passaseo

We deals with nonlinear elliptic Dirichlet problems of the form $${\rm div}(|D u|^{p-2}D u )+f(u)=0\quad\mbox{ in }Ω,\qquad u\in H^{1,p}_0(Ω) $$ where $Ω$ is a bounded domain in $\…

math.AP2018

Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in exterior domains

Sergio Lancelotti, Riccardo Molle

The paper concerns with positive solutions of problems of the type $- Δ u + a (x) u = u^{p - 1} + ε u^{2^{*} - 1}$ in $Ω \subseteq R^{N}$ , $N \geq 3$ , $2^{*} = \frac{2 N}{N - 2}$ , $2<p<2^*…

math.AP2018

Infinitely many positive standing waves for Schrödinger equations with competing coefficients

Giovanna Cerami, Riccardo Molle

The paper deals with the equation $- Δ u + a (x) u + b (x) u^{q} - u^{p} = 0$ , $u \in H^{1} (R^{N})$ , whith $N \geq 2$ , $1 < q < p, p < \frac{N + 2}{N - 2}$ if $N \geq 3$ , $in f a > 0$ , $a (x) \to a_{\infty}$ and $b(x…

math.AP2018★ 1 cited

Multiple positive bound states for critical Schrödinger-Poisson systems

Giovanna Cerami, Riccardo Molle

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrödinger-Poisson system: $$ \left\{ \begin{array}{l…

math.AP2013

Semilinear elliptic problems in unbounded domains with unbounded boundary

Riccardo Molle

This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentra…

math.AP2013

Positive solutions for a nonlinear elliptic problem with strong lack of compactness

Riccardo Molle

This paper deals with the lack of compactness in nonlinear elliptic problems $(P)$ . In particular, a domain $Ω$ is provided where not converging Palais-Smale sequences exist at eve…

math.AP2013

Multiple Solutions for Scalar Field Equations with Potentials having "Subsidences"

Giovanna Cerami, Riccardo Molle, Donato Passaseo

In this paper the question of finding infinitely many solutions to the problem $- Δ u + a (x) u = ∣ u ∣^{p - 2} u$ , in $R^{N}$ , $u \in H^{1} (R^{N})$ , is considered when $N \geq 2$ , $…

Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations

Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains

Positive solutions to nonlinear elliptic problems involving Sobolev exponent

Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation

Standing waves for two-component elliptic system with critical growth in R4: the attractive case

Normalized positive solutions for Schrödinger equations with potentials in unbounded domains

On a planar Schrödinger-Poisson system involving a non-symmetric potential

Variational properties of the first curve of the Fuč\'ık spectrum for elliptic operators

Infinitely many solutions for elliptic equations with non-symmetric nonlinearities

Normalized solutions to mass supercritical Schrodinger equations with negative potential

Normalized solutions of mass supercritical Schrödinger equations with potential

Infinitely many positive solutions of nonlinear Schrodinger equations

Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth

Nonexistence of solutions for Dirichlet problems with supercritical growth in tubular domains

Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains

Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in exterior domains

Infinitely many positive standing waves for Schrödinger equations with competing coefficients

Multiple positive bound states for critical Schrödinger-Poisson systems

Semilinear elliptic problems in unbounded domains with unbounded boundary

Positive solutions for a nonlinear elliptic problem with strong lack of compactness

Multiple Solutions for Scalar Field Equations with Potentials having "Subsidences"

Standing waves for two-component elliptic system with critical growth in $R^{4}$ : the attractive case