16 papers · 1 filter
Ground states for strongly indefinite Schrödinger equations with competing nonlinearities
Bartosz Bieganowski
We survey recent variational methods for strongly indefinite Schrödinger equations with sign-changing nonlinearities. The main object is an energy functional of the form \[ J(u)=\…
Nonlinear Schrödinger equations with a critical, inverse-square potential
Bartosz Bieganowski, Adam Konysz, Simone Secchi
We study the existence of solutions of the following nonlinear Schrödinger equation where and $f:\mat…
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…
Note on the multiplicity of solutions for nonlinear scalar field equations with a critical inverse-square potential
Bartosz Bieganowski, Daniel Strzelecki
We are interested in the multiplicity of solutions to the following scalar field equation $$ -Îu - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\}.…
Nonlinear scalar field equations with a critical Hardy potential
Bartosz Bieganowski, Daniel Strzelecki
We study the existence of solutions for the nonlinear scalar field equation $$-Îu - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\},$$ where the pot…