103 citations · 184 across the 37 of their papers we have counts for
5 papers · 1 filter
Ground state solutions to the nonlinear Born-Infeld problem
Bartosz Bieganowski, Norihisa Ikoma, Jarosław Mederski
In the paper we show the existence of ground state solutions to the nonlinear Born-Infeld problem \[ \mathrm{div}\, \left( \frac{\nabla u}{\sqrt{1-|\nabla u|^2}} \right) + f(u) = 0…
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…
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 $$-Δu - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\},$$ where the pote…
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…
Note on elliptic equations on closed manifolds with singular nonlinearities
Bartosz Bieganowski, Adam Konysz
We consider a general elliptic equation on a closed Riemannian manifold and utilize a recent variational approach by Hebey, Pacard, Pol…