Problems on Elliptic PDEs: systems and equations

• Grant number: 15/17096-6
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2015
• End date: April 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ederson Moreira dos Santos
• Grantee: Ederson Moreira dos Santos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos
• Associated research grant(s): 16/50453-0 - Semilinear and quasilinear elliptic partial differential equations , AP.R SPRINT

Abstract

This project proposes research about problems involving partial differential equations, essentially of elliptic type. It presents questions about existence, multiplicity and qualitative properties of the solutions of problems involving second and fourth orders equations, as well as systems of second order equations. A special attention is addressed to the study of qualitative properties, with emphases on symmetry, concentration, blow up phenomena and asymptotic behaviour of the solutions. (AU)

Scientific publications

(6)

(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)

BONHEURE, DENIS; FOLDES, JURAJ; DOS SANTOS, EDERSON MOREIRA; SALDANA, ALBERTO; TAVARES, HUGO. PATHS TO UNIQUENESS OF CRITICAL POINTS AND APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 370, n. 10, p. 7081-7127, OCT 2018. (14/03805-2, 15/17096-6)

FERREIRA, JR., VANDERLEY; GAZZOLA, FILIPPO; DOS SANTOS, EDERSON MOREIRA. Instability of modes in a partially hinged rectangular plate. Journal of Differential Equations, v. 261, n. 11, p. 6302-6340, DEC 5 2016. (14/03805-2, 15/17096-6, 12/23741-3)

DA SILVA, WENDEL LEITE; DOS SANTOS, EDERSON MOREIRA. Monotonicity of the Morse index of radial solutions of the Henon equation in dimension two. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 48, p. 485-492, AUG 2019. (15/17096-6)

BONHEURE, DENIS; CASTERAS, JEAN-BAPTISTE; DOS SANTOS, EDERSON MOREIRA; NASCIMENTO, ROBSON. ORBITALLY STABLE STANDING WAVES OF A MIXED DISPERSION NONLINEAR SCHRODINGER EQUATION. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 50, n. 5, p. 5027-5071, 2018. (15/17096-6, 16/50453-0)

MERCURI, CARLO; DOS SANTOS, EDERSON MOREIRA. Quantitative symmetry breaking of groundstates for a class of weighted Emden-Fowler equations. Nonlinearity, v. 32, n. 11, p. 4445-4464, NOV 2019. (15/17096-6)

DA SILVA, WENDEL LEITE; DOS SANTOS, EDERSON MOREIRA. Asymptotic profile and Morse index of the radial solutions of the Henon equation. Journal of Differential Equations, v. 287, p. 24-pg., 2021-04-02. (15/17096-6)