Sonata grant: Variational Problems with Singularities Arising from Mathematical Physics
Main scientific tasks of the project
- Einstein scalar field equations of Lichnerowicz type
- Problems on noncompact manifolds
- General singular nonlinearities
- Related Schrödinger and Helmholtz equations on manifolds
- Normalized problems
- Nonlinear, singular Schrödinger equations
- Critical Hardy potentials
- Berestycki-Lions-type problems
- Related curl-curl problems
- Singular problems with fractional and higher-order operators
Scientific team
- Principal Investigator: Bartosz Bieganowski
- Post-doc (from 03.2024 to 02.2026): Daniel Strzelecki
- PhD student (from 10.2024 to 09.2025): Adam Konysz
Collaborators involved in the project
- Laura Baldelli (Institute of Mathematics, University of Granada)
- Pietro d'Avenia (Dipartimento di Meccanica, Matematica e Managemen, Politecnico di Bari)
- Jarosław Mederski (Institute of Mathematics, Polish Academy of Sciences)
- Jacopo Schino (Faculty of Mathematics, Informatics and Mechanics, University of Warsaw)
- Simone Secchi (Dipartimento di Matematica e Applicazioni, Universita' di Milano Bicocca)
Results
- F. Bernini, B. Bieganowski, D. Strzelecki: Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part,
submitted, arXiv:2410.13315 - B. Bieganowski, O.H. Miyagaki, J. Schino: Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities,
submitted, arXiv:2410.05885 - L. Baldelli, B. Bieganowski, J. Mederski: Traveling waves for nonlinear Schrödinger equations,
submitted, arXiv:2406.03910 - F. Bernini, B. Bieganowski, D. Strzelecki: Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part,
submitted, arXiv:2405.20908
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