Existence of solutions for asymptotically linear at infinity systems

• Grant number: 16/20798-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2017
• End date: March 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Sergio Henrique Monari Soares
• Grantee: Raquel Lehrer
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In this project, we present a study proposal for systems of Schrodinger equations wich are asymptotically linear at infinity. Asymptotically linear at infinity problems arise frequently in the nonlinear optics, and have been the topic of many studies of physicists and mathematicians in the last years. However, such studies are mostly dedicated to the study of the scalar case, i.e., problems that consider only one equation. We propose to do a detailed study of a class of asymptotically linear at infinity systems, always searching for the necessary conditions for the determination of positive solutions. Our goal is study such problems using variational methods. The duration of this project is twelve months. (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)

LEHRER, RAQUEL; MONARI SOARES, SERGIO H.. Existence and concentration of positive solutions for a system of coupled saturable Schrodinger equations. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 197, AUG 2020. (16/20798-5)