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Informace o projektu
Nonlinear Schrödinger equations and systems with singular potentials (NSESSP)

Logo poskytovatele
Kód projektu
GA22-17403S
Období řešení
1/2022 - 12/2024
Investor / Programový rámec / typ projektu
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: 9

2024

2023

2022

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