7 papers
An Index Theorem in Relative K-Theory for First-Order Systems
Robert Skiba, Daniel Strzelecki, Nils Waterstraat
Motivated by bifurcation of branches of homoclinic orbits of dynamical systems, we consider families of first-order equations on the real line and introduce a generalisation of pre…
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 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…
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…
Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part
Federico Bernini, Bartosz Bieganowski, Daniel Strzelecki
We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a disl…