37 citations · 83 across the 15 of their papers we have counts for
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A Lagrangian approach for prescribed mass solutions of cubic-quintic Schrödinger equations and -supercritical problems
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
We study the existence of radially symmetric solutions of the following nonlinear scalar field equations in (): $$ (*)_m \quad - Δu + μu = g(u) \quad \text{…
Normalized ground states for NLS equations with mass critical nonlinearities
Silvia Cingolani, Marco Gallo, Norihisa Ikoma +1
We study normalized solutions to nonlinear Schrödinger equations $$ -Δu + μu = g(u)\quad \hbox{in}\ \mathbb{R}^N, \qquad \frac{1}{2}\…
Quantitative and exact concavity principles for parabolic and elliptic equations
Marco Gallo, Riccardo Moraschi, Marco Squassina
Goal of this paper is to study classes of Cauchy-Dirichlet problems which include parabolic equations of the type with $Ω\subse…
A Pohožaev minimization for normalized solutions: fractional sublinear equations of logarithmic type
Marco Gallo, Jacopo Schino
In this paper, we search for normalized solutions to a fractional, nonlinear, and possibly strongly sublinear Schrödinger equation $$(-Δ)^s u + μu = g(u) \quad \hbox{in $\mathbb{R}…
Power law convergence and concavity for the Logarithmic Schrödinger equation
Marco Gallo, Sunra Mosconi, Marco Squassina
We study concavity properties of positive solutions to the Logarithmic Schrödinger equation in a general convex domain with Dirichlet conditions. To this aim, we…
Normalized solutions for nonlinear Schrödinger equations with -critical nonlinearity
Silvia Cingolani, Marco Gallo, Norihisa Ikoma +1
We study the following nonlinear Schrödinger equation and we look for normalized solutions for a given and \[ -Δu + μu = g(u…
Concavity and perturbed concavity for -Laplace equations
Marco Gallo, Marco Squassina
In this paper we study convexity properties for quasilinear Lane-Emden-Fowler equations of the type $$\begin{cases} -Δ_p u = a(x) u^q & \quad \hbox{ in },\\ u >0 & \quad \hbox{…
Asymptotic decay of solutions for sublinear fractional Choquard equations
Marco Gallo
Goal of this paper is to study the asymptotic behaviour of the solutions of the following doubly nonlocal equation …
Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
In this paper we study the following nonlinear fractional Choquard-Pekar equation \begin{equation}\label{eq_abstract} (-Δ)^s u + μu =(I_α*F(u)) F'(u) \quad \hbox{in}\ \mathbb{R}^N,…
Concavity properties for quasilinear equations and optimality remarks
Nouf M. Almousa, Jacopo Assettini, Marco Gallo +1
In this paper we study quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schrödinger equations of the type $$-{\rm div}\big(a(u) \nabla u\b…
On fractional Schrödinger equations with Hartree type nonlinearities
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
Goal of this paper is to study the following doubly nonlocal equation \begin{equation}\label{eq_abstract} (- Δ)^s u + μu = (I_α*F(u))F'(u) \quad \hbox{in } \tag{P} \e…
Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation
Silvia Cingolani, Marco Gallo, Kazunaga Tanaka
We study existence of solutions for the fractional problem \begin{equation*} (P_m) \quad \left \{ \begin{aligned} (-Δ)^{s} u + μu &=g(u) & \; \text{in }, \cr \int_{\m…
Multiplicity and concentration results for local and fractional NLS equations with critical growth
Marco Gallo
Goal of this paper is to study positive semiclassical solutions of the nonlinear Schrödinger equation where…
On the fractional NLS equation and the effects of the potential well's topology
Silvia Cingolani, Marco Gallo
In this paper we consider the fractional nonlinear Schrödinger equation where , , $V \in…