103 citations · 184 across the 37 of their papers we have counts for
40 papers
Explicit counterexamples to Frank-Loss optimizer conjectures for critical Dirac and vector Sobolev inequalities
Bartosz Bieganowski, Jarosław Mederski
Frank and Loss proposed critical Sobolev inequalities for the Dirac operator and for vector fields. They conjectured optimality of their spinorial family and wrote that it is conce…
Existence of solutions for a large defocusing parameter in a strongly indefinite Schrödinger equation
Bartosz Bieganowski
Let , , and let be real-valued and -periodic. We assume that belongs to a finite spectral gap of the periodic Sc…
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)=\f…
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…
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:\mathb…