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Existence of solutions for asymptotically linear at infinity systems

Grant number: 16/20798-5
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): April 01, 2017
Effective date (End): March 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Acordo de Cooperação: 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)

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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, . (16/20798-5)

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