| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] IME USP, Dept Math, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | Advances in Differential Equations; v. 23, n. 11-12, p. 793-846, NOV-DEC 2018. |
| Web of Science Citations: | 2 |
| Abstract | |
The aim of this work is to demonstrate the effectiveness of the extension theory of symmetric operators in the investigation of the stability of standing waves for the nonlinear Schrodinger equations with two types of non-linearities (power and logarithmic) and two types of point interactions (delta-and delta `-) on a star graph. Our approach allows us to overcome the use of variational techniques in the investigation of the Morse index for self-adjoint operators with non-standard boundary conditions which appear in the stability study. We also demonstrate how our method simplifies the proof of the stability results known for the NLS equation with point interactions on the line. (AU) | |
| FAPESP's process: | 16/02060-9 - Application of the theory of extensions to the spectral analysis of some self-adjoint operators |
| Grantee: | Nataliia Goloshchapova |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/50503-6 - Boundary triplet theory and its applications to spectral theory of differential operators with point interactions and nonlinear Schrödinger equations with potentials of $ / delta $ - $ delta $ type |
| Grantee: | Nataliia Goloshchapova |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/07311-0 - Schrodinger equations with point interactions and instability for the fractional Korteweg- de Vries equation |
| Grantee: | Jaime Angulo Pava |
| Support Opportunities: | Scholarships abroad - Research |