22 citations · 50 across the 18 of their papers we have counts for
18 papers
A generalisation of the Gagliardo--Nirenberg Inequality with applications to mass-critical and mass-subcritical elliptic equations
Bartosz Bieganowski, Jacopo Schino
Via a new inequality à la Gagliardo--Nirenberg, we prove the existence and nonexistence of solutions to \begin{equation*} \begin{cases} (-Δ)^s u + \fracμ{|y|^{2s}} u + λu = f(u), \…
Finite-energy solutions to Einstein-scalar field Lichnerowicz equations on complete Riemannian manifolds
Bartosz Bieganowski, Pietro d'Avenia, Jacopo Schino
We consider the singular elliptic problem of the form \[ -Δu + V(x)u = \mathcal{B}(x)|u|^{2^*-2}u + \frac{\mathcal{A}(x)}{|u|^{2^*}u}, \qquad u\in H^1(M), \] where the coefficients…
A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds
Bartosz Bieganowski, Pietro d'Avenia, Jacopo Schino +1
In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-con…
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}…
Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities
Bartosz Bieganowski, Olímpio Hiroshi Miyagaki, Jacopo Schino
Via a constrained minimization, we find a solution to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|x|^{2m}}u + λu = ηu^3 + g(u)\\ \int_{\mathbb{R}^{2m}} u^2…
Some one-dimensional elliptic problems with constraints
Jacopo Schino, Panayotis Smyrnelis
Given and , we find solutions to the problem \begin{equation*} \begin{cases} \bigl(-\frac{\mathrm{d}^2}{\mathrm{d} x^2}\bigr)^m u +…
Piecewise regular solutions to scalar balance laws with singular nonlocal sources
Lorena Bociu, Evangelia Ftaka, Khai T. Nguyen +1
The present paper establishes a local well-posed result for piecewise regular solutions with single shock of scalar balance laws with singular integral of convolution type kernels.…
Travelling waves for Maxwell's equations in nonlinear and symmetric media
Jarosław Mederski, Jacopo Schino
We look for travelling wave fields satisfying Maxwell's equations…
Existence and dynamics of normalized solutions to Schrödinger equations with generic double-behaviour nonlinearities
Bartosz Bieganowski, Pietro d'Avenia, Jacopo Schino
We study the existence of solutions to \[ -Δu + λu = f(u) \quad \text{in } \mathbb{R}^N \] with…
Normalized solutions to Schrödinger equations in the strongly sublinear regime
Jarosław Mederski, Jacopo Schino
We look for solutions to the Schrödinger equation \[ -Δu + λu = g(u) \quad \text{in } \mathbb{R}^N \] coupled with the mass constraint , with $N…
Normalized solutions to at least mass critical problems: singular polyharmonic equations and related curl-curl problems
Bartosz Bieganowski, Jarosław Mederski, Jacopo Schino
We are interested in the existence of normalized solutions to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|y|^{2m}}u + λu = g(u), \quad x = (y,z) \in \mathbb{R}^K \…
Ground state, bound state, and normalized solutions to semilinear Maxwell and Schrödinger equations
Jacopo Schino
The existence of ground states and (multiple) bound states to semilinear time-independent Maxwell and Schrödinger equations, with or without -constraints, is investigated.
Radial and non-radial multiple solutions to a general mixed dispersion NLS equation
Pietro d'Avenia, Alessio Pomponio, Jacopo Schino
We study the following nonlinear Schrödinger equation with a forth order dispersion term \[ Δ^2u-βΔu=g(u) \quad \text{in } \mathbb{R}^N \] in the positive and zero mass regimes: in…
Nonlinear curl-curl problems in
Jarosław Mederski, Jacopo Schino
We survey recent results concerning ground states and bound states to the curl-curl problem $$\nabla\times(\nabla\times u)+V(x)u= f(x,u) \quad\…
Normalized ground states to a cooperative system of Schrödinger equations with generic -subcritical or -critical nonlinearity
Jacopo Schino
We look for ground state solutions to the Schrödinger-type system \[ \begin{cases} -Δu_j + λ_j u_j = \partial_jF(u)\\ \int_{\rn} u_j^2 \, dx = a_j^2\\ (λ_j,u_j) \in \mathbb{R} \tim…
Least energy solutions to a cooperative system of Schrödinger equations with prescribed -bounds: at least -critical growth
Jarosław Mederski, Jacopo Schino
We look for least energy solutions to the cooperative systems of coupled Schrödinger equations \begin{equation*} \begin{cases} -Δu_i + λ_i u_i = \partial_iG(u)\quad \mathrm{in} \ \…
Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials
Michał Gaczkowski, Jarosław Mederski, Jacopo Schino
We look for multiple solutions to the curl-curl problem \[ \nabla\times\nabla\times\mathbf{U}=h(x,\mathbf{U}),\qquad x\in\mathbb{R}^3,…
Multiple solutions to a nonlinear curl-curl problem in
Jarosław Mederski, Jacopo Schino, Andrzej Szulkin
We look for ground states and bound states to the curl-curl problem which ori…