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

• Grant number: 12/50503-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): January 01, 2013
• Effective date (End): November 25, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Jaime Angulo Pava
• Grantee: Nataliia Goloshchapova
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project is principally aimed to demonstrate efficiency of boundary triplets and the corresponding Weyl functions approach for the investigation of certain spectral characteristics of differential operators with point interactions. We also plan to apply boundary triplets approach for investigation of non-linear Schrodinger equation with periodic and non-periodic $\delta$-potential and the problem of the existence and stability of standing waves for such non-linear Schrodinger models, i.e. stability study for the "standing-peak" solutions. The importance of investigation of such objects is due to their applications in quantum mechanics and Bose-Einstein condensates. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PAVA, JAIME ANGULO; GOLOSHCHAPOVA, NATALIIA. EXTENSION THEORY APPROACH IN THE STABILITY OF THE STANDING WAVES FOR THE NLS EQUATION WITH POINT INTERACTIONS ON A STAR GRAPH. Advances in Differential Equations, v. 23, n. 11-12, p. 793-846, NOV-DEC 2018. (16/02060-9, 12/50503-6, 16/07311-0)

ANANIEVA, ALEKSANDRA; GOLOSHCHAPOVA, NATALY. ON THE EXTREMAL EXTENSIONS OF A NON-NEGATIVE JACOBI OPERATOR. METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, v. 19, n. 4, p. 9-pg., 2013-01-01. (12/50503-6)

PAVA, JAIME ANGULO; GOLOSHCHAPOVA, NATALIIA. Stability of standing waves for NLS-log equation with delta-interaction. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 24, n. 3, JUN 2017. (16/02060-9, 12/50503-6)