Aspects of Nonlinear Elliptic Equations and Systems

• Grant number: 16/15887-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: October 01, 2016
• End date: March 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Djairo Guedes de Figueiredo
• Grantee: José Vitor Pena
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 17/26582-7 - Weighted Trudinger-Moser inequalities on unbounded domains, BE.EP.DR

Abstract

The focus of the project is the study of solutions of elliptic differential partial equations and systems and its properties, such as existence, multiplicity and regularity. Some important techniques that emerge naturally from these problems will be studied and applied to a specific problem. The principal tools are: variational methods (e.g. The Mountain Pass Theorem) and topological methods (e.g. Brouwer and Leray-Schauder Degree Thoery). Other tools that might be studied are Lusternik-Schneillmann Theory, Morse Theory on Banach Spaces and Kranoselski-Rabinowitz Bifurcation Theory.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

PENA, José Vitor. Atingibilidade de supremos do tipo Trudinger-Moser e problemas do tipo Henón relacionados. 2020. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.