10 papers · 1 filter
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 \[ -Îu + V(x)u = \mathcal{B}(x)|u|^{2^*-2}u + \frac{\mathcal{A}(x)}{|u|^{2^*}u}, \qquad u\in H^1(M), \] where the coefficient…
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…
Travelling waves for Maxwell's equations in nonlinear and symmetric media
JarosÅaw Mederski, Jacopo Schino
We look for travelling wave fields satisfying Maxwell's equatio…
Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities
Bartosz Bieganowski, OlÃmpio Hiroshi Miyagaki, Jacopo Schino
Via a constrained minimization, we find a solution to the problem \begin{equation*} \begin{cases} (-Î)^m u+\fracμ{|x|^{2m}}u + λu = ηu^3 + g(u)\\ \int_{\mathbb{R}^{2m}…
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 \[ -Îu + λu = f(u) \quad \text{in } \mathbb{R}^N \] w…