Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Nonlinear equations involving the curl-curl operator

2017/26/E/ST1/00817

Keywords:

curl-curl operator Maxwell equations Born-Infeld theory variational methods bifurcation theory critical point theory

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_12: Mathematical methods of physics

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Instytut Matematyczny Polskiej Akademii Nauk

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Jarosław Mederski 

Number of co-investigators in the project: 4

Call: SONATA BIS 7 - announced on 2017-06-14

Amount awarded: 1 090 012 PLN

Project start date (Y-m-d): 2018-08-01

Project end date (Y-m-d): 2023-11-30

Project duration:: 64 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Komputer przenośny (laptop) (7 000 PLN)

Information in the final report

  • Publication in academic press/journals (24)
  1. Connecting orbits in Hilbert spaces and applications to P.D.E.
    Authors:
    Panayotis Smyrnelis
    Academic press:
    Communications on Pure and Applied Analysis (rok: 2020, tom: 19, No. 5, strony: 2797–2818), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/cpaa.2020122 - link to the publication
  2. Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system
    Authors:
    Michał Kowalczyk, Xavier Lamy, Panayotis Smyrnelis
    Academic press:
    Archive for Rational Mechanics and Analysis (rok: 2022, tom: 245, strony: 565-586), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00205-022-01794-0 - link to the publication
  3. Least energy solutions to a cooperative system of Schrödinger equations with prescribed L^2-bounds: at least L^2-critical growth
    Authors:
    Jarosław Mederski, Jacopo Schino
    Academic press:
    Calculus of Variations and Partial Differential Equations (rok: 2022, tom: 2,54861111111111, strony: 10), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-021-02116-0 - link to the publication
  4. Multiple Solutions to a Nonlinear Curl–Curl Problem in R^3
    Authors:
    Jarosław Mederski, Jacopo Schino, Andrzej Szulkin
    Academic press:
    Archive for Rational Mechanics and Analysis (rok: 2020, tom: 236, strony: 253-288), Wydawca: Springer Berlin Heidelberg
    Status:
    Published
    DOI:
    10.1007/s00205-019-01469-3 - link to the publication
  5. Normalized ground states to a cooperative system of Schrödinger equations with generic L2-subcritical or L2-critical nonlinearity
    Authors:
    Jacopo Schino
    Academic press:
    Advances in Differential Equations (rok: 2022, tom: 27, no.7-8,, strony: 467-496), Wydawca: Khayyam Publishing
    Status:
    Published
    DOI:
    10.57262/ade027-0708-467 - link to the publication
  6. Born-Infeld problem with general nonlinearity
    Authors:
    Alessio Pomponio, Jarosław Mederski
    Academic press:
    Journal of Differential Equations (rok: 2023, tom: 370, strony: 470-497), Wydawca: Elselvier
    Status:
    Published
    DOI:
    10.1016/j.jde.2023.06.030 - link to the publication
  7. On the origin of the optical vortex lattices in a nematic liquid crystal light valve
    Authors:
    Enrique Calisto, Marcel G. Clerc, Michał Kowalczyk, Panayotis Smyrnelis
    Academic press:
    Optics Letters (rok: 2019, tom: 44 No. 12, strony: 2947–2950), Wydawca: OSA Publishing
    Status:
    Published
    DOI:
    10.1364/OL.44.002947 - link to the publication
  8. Normalized solutions to Born-Infeld and quasilinear problems
    Authors:
    Laura Baldelli, Jaroslaw Mederski, Alessio Pomponio
    Academic press:
    Journal of Differential Equations , Wydawca: Academic Press Inc.
    Status:
    Submitted
    DOI:
    brak - link to the publication
  9. Normalized solutions to Schrödinger equations in the strongly sublinear regime
    Authors:
    Jarosław Mederski, Jacopo Schino
    Academic press:
    Calculus of Variations and Partial Differential Equations , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  10. Biharmonic Nonlinear Scalar Field Equations
    Authors:
    Jarosław Mederski, Jakub Siemianowski
    Academic press:
    International Mathematics Research Notices (rok: 2023, tom: 2023 No. 23, strony: 19963-19995), Wydawca: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/imrn/rnac303 - link to the publication
  11. Bound states for the Schrödinger equation with mixed-type nonlinearites
    Authors:
    Bartosz Bieganowski, Jarosław Mederski
    Academic press:
    Indiana University Mathematics Journal (rok: 2022, tom: 71 No. 1, strony: 65-92), Wydawca: Indiana University
    Status:
    Published
    DOI:
    10.1512/iumj.2022.71.8662 - link to the publication
  12. Elliptic problems with mixed nonlinearities and potentials singular at the origin and at the boundary of the domain
    Authors:
    Bartosz Bieganowski, Adam Konysz
    Academic press:
    Journal of Fixed Point Theory and Applications (rok: 2023, tom: 25:83, strony: 25:83), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11784-023-01085-5 - link to the publication
  13. Nonlinear curl-curl problems in R^3
    Authors:
    Jacopo Schino, Jarosław Mederski
    Academic press:
    Minimax Theory and its Applications (rok: 2022, tom: 7, No. 2, strony: 339–364), Wydawca: Heldermann
    Status:
    Published
    DOI:
    brak - link to the publication
  14. Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth
    Authors:
    Bartosz Bieganowski, Jarosław Mederski
    Academic press:
    Journal of Functional Analysis (rok: 2021, tom: 280 (11), strony: 108989), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2021.108989 - link to the publication
  15. A Sobolev-Type Inequality for the Curl Operator and Ground States for the Curl–Curl Equation with Critical Sobolev Exponent
    Authors:
    Jarosław Mederski, Andrzej Szulkin
    Academic press:
    Archive for Rational Mechanics and Analysis (rok: 2021, tom: 241, strony: 1815-1842), Wydawca: Springer Berlin Heidelberg
    Status:
    Published
    DOI:
    10.1007/s00205-021-01684-x - link to the publication
  16. General class of optimal Sobolev inequalities and nonlinear scalar field equations
    Authors:
    Jarosław Mederski
    Academic press:
    Journal of Differential Equations (rok: 2021, tom: 281, strony: 411-441), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2021.02.015 - link to the publication
  17. Nonlinear scalar field equation with competing nonlocal terms
    Authors:
    Pietro d'Avenia, Jarosław Mederski, Alessio Pomponio
    Academic press:
    Nonlinearity (rok: 2021, tom: 34, strony: 5687-5707), Wydawca: IOP Publishing and the London Mathematical Society
    Status:
    Published
    DOI:
    10.1088/1361-6544/ac0d47 - link to the publication
  18. Vortex filament solutions in the Ginzburg-Landau-Painlevé theory of phase transition
    Authors:
    Panayotis Smyrnelis
    Academic press:
    Journal de Mathématiques Pures et Appliquées (rok: 2021, tom: 156, strony: 328-350), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.matpur.2021.05.003 - link to the publication
  19. Brezis--Kato Type Regularity Results for Higher Order Elliptic Operators
    Authors:
    Jakub Siemianowski
    Academic press:
    Topological Methods in Nonlinear Analysis , Wydawca: UMK
    Status:
    Submitted
    DOI:
    brak - link to the publication
  20. Double layered solutions to the extended Fisher-Kolmogorov P.D.E.
    Authors:
    Panayotis Smyrnelis
    Academic press:
    Nonlinear Differential Equations and Applications (rok: 2021, tom: 1,2, strony: 5,13427), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00030-021-00708-5 - link to the publication
  21. Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials
    Authors:
    Michał Gaczkowski, Jarosław Mederski, Jacopo Schino
    Academic press:
    SIAM Journal on Mathematical Analysis (rok: 2023, tom: 55(5), strony: 4425-4444), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/22M1494786 - link to the publication
  22. Between Maxwell and Born-Infeld: the presence of the magnetic field
    Authors:
    Pietro d'Avenia, Jarosław Mederski
    Academic press:
    Annales de l'Institut Henri Poincaré, Analyse Non Linéaire , Wydawca: EMS Press
    Status:
    Submitted
    DOI:
    brak - link to the publication
  23. Normalized solutions to at least mass critical problems: singular polyharmonic equations and related curl-curl problems
    Authors:
    Bartosz Bieganowski, Jarosław Mederski, Jacopo Schino
    Academic press:
    Mathematische Annalen , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  24. Semiclassical states for the curl-curl problem
    Authors:
    Bartosz Bieganowski, Adam Konysz, Jarosław Mederski
    Academic press:
    SIAM Journal on Mathematical Analysis , Wydawca: SIAM
    Status:
    Submitted
    DOI:
    brak - link to the publication

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