Uniqueness of Solutions to Nonlinear Schrödinger Equations from their Zeros.
Ann PDE
; 8(2): 21, 2022.
Article
em En
| MEDLINE
| ID: mdl-36119810
ABSTRACT
We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution u = 0 is the only solution for which the assumptions u ( t = 0 ) | D = 0 , u ( t = T ) | D = 0 hold, where D â R d are certain subsets of codimension one. In particular, D is discrete for dimension d = 1 . Our main theorem can be seen as a nonlinear analogue of discrete Fourier uniqueness pairs such as the celebrated Radchenko-Viazovska formula in [21], and the uniqueness result of the second author and M. Sousa for powers of integers [22]. As an additional application, we deduce rigidity results for solutions to some semilinear elliptic equations from their zeros.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Ann PDE
Ano de publicação:
2022
Tipo de documento:
Article