Informace o projektu
Nonlinear Schrödinger equations and systems with singular potentials
(NSESSP)
- Kód projektu
- GA22-17403S
- Období řešení
- 1/2022 - 12/2024
- Investor / Programový rámec / typ projektu
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Grantová agentura ČR
- Standardní projekty
- Fakulta / Pracoviště MU
- Přírodovědecká fakulta
The research of nonlinear Schrödinger (NLS) equations and systems has been attracted a great deal of attention from mathematicians in the field of partial differential equations because of its application in quantum mechanics. A huge literature has been devoted to the study of NLS equations and systems with a singular potential. The presence of the singular potential yields distinctive features of the study and leads to the disclosure of new phenomena. The borderline case when the potential scales the same as the Laplacian has not been well explored and cannot be tackled simply by perturbation methods; hence innovative approaches are required. In this project, we propose to study two closely related problems involving a critical potential: the boundary value problem with measure data for nonlinear time-independent Schrödinger equations and the Cauchy problem for nonlinear time-dependent Schrödinger systems.
Publikace
Počet publikací: 5
2024
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Semilinear elliptic Schrödinger equations involving singular potentials and source terms
Nonlinear Analysis, rok: 2024, ročník: 238, vydání: January, DOI
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Semilinear elliptic Schrödinger equations with singular potentials and absorption terms
Journal of the London Mathematical Society, rok: 2024, ročník: 109, vydání: 1, DOI
2023
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Existence and Multiplicity Results for Nonlocal Lane-Emden Systems
Acta Mathematica Vietnamica, rok: 2023, ročník: 48, vydání: 1, DOI
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Poisson problems involving fractional Hardy operators and measures
Nonlinearity, rok: 2023, ročník: 36, vydání: 12, DOI
2022
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On critical double phase Kirchhoff problems with singular nonlinearity
Rendiconti del Circolo Matematico di Palermo Series 2, rok: 2022, ročník: 71, vydání: 3, DOI