Nonlinear Schrödinger equations and systems with singular potentials (NSESSP)

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Project Identification
Project Period
1/2022 - 12/2024
Investor / Pogramme / Project type
Czech Science Foundation
MU Faculty or unit
Faculty of Science

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.


Total number of publications: 2

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