Perturbation problems and semilinear elliptic equations

• Grant number: 18/21554-8
• Support Opportunities: Regular Research Grants
• Duration: February 01, 2019 - April 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Sérgio Leandro Nascimento Neves
• Grantee: Sérgio Leandro Nascimento Neves
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated researchers: angela pistoia ; Francesca Gladiali ; Heloísa Lopes de Sousa ; massimo grossi

Abstract

In this project we study applications of nonlinear analysis techniques to semilinear elliptic equations such as the Brezis-Nirenberg problem, the Coron's problem, the Hénon equation and possibly other related models. Regarding the case of problems with subcritical nonlinearity we are interested in combine variational methods and perturbation methods to prove the existence of solutions. As for the case of problems with supercritical nonlinearity we plan to apply bifurcation theory and perturbation methods to prove the existence of solutions. Moreover, we are interested in some properties of these solutions such as: asymptotic behaviour, symmetry type, Morse index and decay rate for problems in unbounded domains. To deal with some of these problems we intend to develop new techniques and adapt the perturbation methods to treat the degenerate case where the classical method does not apply. (AU)