TESdE: Thematic on Equations and Systems of differential Equations

• Grant number: 22/16407-1
• Support Opportunities: Research Projects - Thematic Grants
• Start date: October 01, 2023
• End date: September 30, 2028
• 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
• Pesquisadores principais: Marcos Tadeu de Oliveira Pimenta ; Olimpio Hiroshi Miyagaki
• Associated researchers: Adilson Eduardo Presoto ; Djairo Guedes de Figueiredo ; Eugenio Tommaso Massa ; Francisco Odair Vieira de Paiva ; Gaetano Siciliano ; Gustavo Ferron Madeira ; Marcos Tadeu de Oliveira Pimenta ; Sergio Henrique Monari Soares ; Sérgio Leandro Nascimento Neves ; Vanderley Alves Ferreira Junior
• Associated research grant(s): 23/14636-6 - Gradient estimates and hopf-Oleinik lemma for quasilinear non-uniformly elliptic operators and applications, AV.BR
• Associated scholarship(s): 25/03040-0 - Fourth-Order Ordinary Differential Equations with Applications in Physics and Mechanics, BP.IC; 24/20593-0 - Qualitative properties for solutions of problems involving elliptic equations, BP.PD; 24/04098-0 - Prescribed elliptical problems, without symmetry in the RN and in unlimited domains: Existence and multiplicity of nodal solutions, BP.DR; + associated scholarships 24/05733-0 - Semilinear equations with absorption nonlinearities and measures as data, BP.MS; 24/15858-5 - Initiation to Variational Inequalities, BP.IC; 24/14947-4 - Introduction to variational methods, BP.IC; 24/04864-4 - Analytic functions and the fluid dynamics, BP.IC; 24/02878-8 - Non-standard analysis, Ultrafunçtions, infinites and infinitesimals, with applications, BP.IC; 24/02669-0 - Study of mean curvature problems by elliptic regularization, BP.MS; 24/03431-7 - Shape optimization and Brouwer topological degree, BP.IC - associated scholarships

Abstract

This project is dedicated to the study of problems involving partial differential equations (PDEs) of elliptic and evolution type, which may include non-local terms. It points questions about the existence and multiplicity and also about qualitative properties, such as symmetry, bifurcation, decay, energy, unique continuation principles, concentration, blow up, and stability of solutions to problems involving second and fourth orders PDEs, as well as second-order systems of PDEs. This project also intersects the areas of functional analysis, differential geometry, ordinary differential equations (ODEs) and numerical simulations for the study of ODEs and PDEs. (AU)

Scientific publications

(12)

(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)

BOER, EDUARDO; DOS SANTOS, EDERSON MOREIRA. Standing waves for nonlinear Hartree type equations: existence and qualitative properties. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 64, n. 5, p. 36-pg., 2025-06-01. (22/16407-1, 23/05445-2)

MOREIRA, DIEGO; SANTOS, JEFFERSON ABRANTES; SOARES, SERGIO H. MONARI. A quantitative version of the Hopf-Oleinik lemma for a quasilinear non-uniformly elliptic operator. ANNALES FENNICI MATHEMATICI, v. 49, n. 1, p. 12-pg., 2024-01-01. (22/16407-1, 23/14636-6)

BARBOZA, EUDES M.; MIYAGAKI, OLIMPIO H.; PEREIRA, FABIO R.; SANTANA, CLAUDIA R.. Hardy-Henon fractional equation with nonlinearities involving exponential critical growth. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, v. 28, n. 1, p. 39-pg., 2024-12-04. (22/16407-1)

LI, HAOYU; MIYAGAKI, OLIMPIO HIROSHI. A Liouville-type theorem for the coupled Schrodinger systems and the uniqueness of the sign-changing radial solutions. Journal of Mathematical Analysis and Applications, v. 539, n. 2, p. 11-pg., 2024-07-05. (22/16407-1, 22/15812-0)

RAMOS QUOIRIN, HUMBERTO; SICILIANO, GAETANO; SILVA, KAYE. Critical points with prescribed energy for a class of functionals depending on a parameter: existence, multiplicity and bifurcation results. Nonlinearity, v. 37, n. 6, p. 40-pg., 2024-06-03. (22/16407-1)

JIANG, QIAOYUN; LI, LIN; CHEN, SHANGJIE; SICILIANO, GAETANO. GROUND STATE SOLUTIONS FOR NONLINEAR SCHRODINGER-BOPP-PODOLSKY BOPP-PODOLSKY SYSTEMS WITH NONPERIODIC POTENTIALS. Electronic Journal of Differential Equations, v. 2024, n. 43, p. 25-pg., 2024-08-12. (22/16097-2, 22/16407-1)

RAMOS, GUSTAVO DE PAULA; SICILIANO, GAETANO. Existence and Concentration of Semiclassical Bound States for a Quasilinear Schrodinger-Poisson System. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, v. 47, n. 6, p. 26-pg., 2024-11-01. (22/16097-2, 22/16407-1)

CARLOS, ROMULO D.; DE OLIVEIRA, VICTOR C.; MIYAGAKI, OLIMPIO H.. Existence and multiplicity of solutions for p-Laplacian fractional system with logarithmic nonlinearity. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 2, p. 32-pg., 2025-01-01. (22/16407-1)

HERNANDEZ, LORENA SORIANO; SICILIANO, GAETANO. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO EIGENVALUE PROBLEMS FOR SCHRÓDINGER-BOPP-PODOLSKY EQUATIONS. Electronic Journal of Differential Equations, v. 2023, n. 66, p. 18-pg., 2023-10-13. (22/16407-1)

DAMIAN, HEYDY M. SANTOS; SICILIANO, GAETANO. Critical Schrodinger-Bopp-Podolsky systems: solutions in the semiclassical limit. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 63, n. 6, p. 23-pg., 2024-07-01. (22/16407-1)

MADEIRA, GUSTAVO FERRON; MIYAGAKI, OLIMPIO HIROSHI; PUCCI, PATRIZIA. Elliptic equations in R^N involving Sobolev supercritical and upper Hardy-Littlewood-Sobolev critical exponents. Journal of Differential Equations, v. 425, p. 26-pg., 2025-01-20. (22/16407-1)

LI, HAOYU; MAIA, BRAULIO B. V.; MIYAGAKI, OLIMPIO H.. Existence of two normalized solutions for a Choquard equation with exponential growth and an L²-subcritical perturbation. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 75, n. 6, p. 19-pg., 2024-12-01. (22/16407-1, 23/09656-8, 22/15812-0)