18 papers
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…
Putnam-like dataset summary: LLMs as mathematical competition contestants
Bartosz Bieganowski, Daniel Strzelecki, Robert Skiba +1
In this paper we summarize the results of the Putnam-like benchmark published by Google DeepMind. This dataset consists of 96 original problems in the spirit of the Putnam Competit…
Explainable Patterns in Cryptocurrency Microstructure
Bartosz Bieganowski, Robert Ålepaczuk
We document stable cross-asset patterns in cryptocurrency limit-order-book microstructure: the same engineered order book and trade features exhibit remarkably similar predictive i…