4 papers
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 $$ -Δu - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\}. $…
A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds
Bartosz Bieganowski, Pietro d'Avenia, Jacopo Schino +1
In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-con…
Nonlinear scalar field equations with a critical Hardy potential
Bartosz Bieganowski, Daniel Strzelecki
We study the existence of solutions for the nonlinear scalar field equation $$-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…