Critical nonlocal quasilinear problem: existence, multiplicity and properties of the solutions

• Grant number: 19/24901-3
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2020
• End date: August 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Olimpio Hiroshi Miyagaki
• Grantee: Olimpio Hiroshi Miyagaki
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Djairo Guedes de Figueiredo ; Francisco Odair Vieira de Paiva ; Gustavo Ferron Madeira ; Marcos Tadeu de Oliveira Pimenta

Abstract

In this project is studied a class of the degenerate quasi-linear problems or critical nonlocal problems with Hardy potential. Multiplicity results will be studied, as well as the existence of nodal solutions as part of their properties. Another class of equations refers to the semilinear equation involving the gradient operator, also with critical power. Existence results will be considered. (AU)

Scientific publications

(22)

(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)

BUENO, HAMILTON P.; CAQUI, EDUARDO HUERTO; MIYAGAKI, OLIMPIO H.. Critical fractional elliptic equations with exponential growth. JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, MAR 2021. (19/24901-3)

BARBOZA, EUDES M.; MIYAGAKI, OLIMPIO H.; PEREIRA, FABIO R.; SANTANA, CLAUDIA R.. HENON EQUATION WITH NOLINEARITIES INVOLVING SOBOLEV CRITICAL GROWTH IN H-0,rad(1)(B-1). Electronic Journal of Differential Equations, p. 1-18, MAR 29 2021. (19/24901-3)

BUENO, H. P.; HUERTO CAQUI, E.; MIYAGAKI, O. H.; PEREIRA, F. R.. Critical Concave Convex Ambrosetti-Prodi Type Problems for Fractional p-Laplacian. ADVANCED NONLINEAR STUDIES, v. 20, n. 4, p. 847-865, NOV 2020. (19/24901-3)

ALVES, CLAUDIANOR O.; JI, CHAO; MIYAGAKI, OLIMPIO H.. Normalized solutions for a Schrodinger equation with critical growth in R-N. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 61, n. 1, FEB 2022. (19/24901-3)

MAIA, B. B. V.; MIYAGAKI, O. H.. Existence and nonexistence results for a class of Hamiltonian Choquard-type elliptic systems with lower critical growth on R-2. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. 152, n. 6, p. 28-pg., 2021-09-28. (19/24901-3)

BARBOZA, EUDES M.; MIYAGAKI, OLIMPIO H.; PEREIRA, FABIO R.; SANTANA, CLAUDIA R.. NONLOCAL HENON EQUATION WITH NONLINEARITIES INVOLVING SOBOLEV CRITICAL AND SUPERCRITICAL GROWTH. Advances in Differential Equations, v. 27, n. 7-8, p. 29-pg., 2022-07-01. (19/24901-3)

BHAKTA, MOUSOMI; CHAKRABORTY, SOUPTIK; MIYAGAKI, OLIMPIO H.; PUCCI, PATRIZIA. Fractional elliptic systems with critical nonlinearities. Nonlinearity, v. 34, n. 11, p. 7540-7573, NOV 2021. (19/24901-3)

DE PAIVA, FRANCISCO ODAIR; DE SOUZA LIMA, SANDRA MACHADO; MIYAGAKI, OLIMPIO HIROSHI. Nehari manifold for a Schrodinger equation with magnetic potential involving sign-changing weight function. APPLICABLE ANALYSIS, v. N/A, p. 28-pg., 2023-06-29. (17/16108-6, 19/24901-3)

DE PAIVA, FRANCISCO ODAIR; LIMA, SANDRA MACHADO DE SOUZA; MIYAGAKI, OLIMPIO HIROSHI. EXISTENCE OF AT LEAST FOUR SOLUTIONS FOR SCHRODINGER EQUATIONS WITH MAGNETIC POTENTIAL INVOLVING AND SIGN-CHANGING WEIGHT FUNCTION. Electronic Journal of Differential Equations, v. 2023, n. 47, p. 16-pg., 2023-07-11. (19/24901-3)

CARRIAO, PAULO CESAR; MIYAGAKI, OLIMPIO HIROSHI; VICENTE, ANDRE. Exponential decay for semilinear wave equation with localized damping in the hyperbolic space. Mathematische Nachrichten, v. 296, n. 1, p. 22-pg., 2022-11-01. (19/24901-3)

LEDESMA, CESAR T.; MIYAGAKI, OLIMPIO H.. Positive Solutions for a Class of Fractional Choquard Equation in Exterior Domain. Milan Journal of Mathematics, v. 90, n. 2, p. 36-pg., 2022-07-06. (19/24901-3)

DE PAIVA, FRANCISCO ODAIR; DE SOUZA LIMA, SANDRA MACHADO; MIYAGAKI, OLIMPIO HIROSHI. Existence and Multiplicity Results for a Class of Nonlinear Schrodinger Equations with Magnetic Potential Involving Sign-Changing Nonlinearity. ANALYSIS IN THEORY AND APPLICATIONS, v. 38, n. 2, p. 30-pg., 2022-01-01. (19/24901-3, 17/16108-6)

MIYAGAKI, O. H.; SANTANA, C. R.; TOON, E.; UBILLA, P.. Critical and subcritical fractional Hamiltonian systems of Schrodinger equations with vanishing potentials. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 229, p. 18-pg., 2023-01-07. (19/24901-3)

ALVES, CLAUDIANOR O.; BOER, EDUARDO DE S.; MIYAGAKI, OLIMPIO H.. EXISTENCE OF NORMALIZED SOLUTIONS FOR THE PLANAR SCHR & Oacute; DINGER-POISSON SYSTEM WITH EXPONENTIAL CRITICAL NONLINEARITY. DIFFERENTIAL AND INTEGRAL EQUATIONS, v. 36, n. 11-12, p. 24-pg., 2023-11-01. (19/22531-4, 19/24901-3)

DE OLIVEIRA, JOSE FRANCISCO; MIYAGAKI, OLIMPIO H.; MOREIRA, I, SANDRA. On a class of degenerate quasilinear elliptic equations with zero mass. Complex Variables and Elliptic Equations, JUL 2021. (19/24901-3)

COSTA, AUGUSTO C. R.; MIYAGAKI, OLIMPIO H.; PEREIRA, FABIO R.. On a nonlocal elliptic system of Hardy-Kirchhoff type with critical exponents. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 46, n. 1, p. 13-pg., 2022-07-11. (19/24901-3)

MIYAGAKI, OLIMPIO H.; SANTANA, CLAUDIA R.; VIEIRA, RONEI S.. SCHRODINGER EQUATIONS IN R-4 INVOLVING THE BIHARMONIC OPERATOR WITH CRITICAL EXPONENTIAL GROWTH. Rocky Mountain Journal of Mathematics, v. 51, n. 1, p. 243-263, FEB 2021. (19/24901-3)

MARCIAL, MARCOS R.; MIYAGAKI, OLIMPIO H.; PEREIRA, GILBERTO A.. TOPOLOGICAL STRUCTURE OF THE SOLUTION SET FOR A FRACTIONAL p-LAPLACIAN PROBLEM WITH SINGULAR NONLINEARITY. Electronic Journal of Differential Equations, v. 2022, n. 60, p. 19-pg., 2022-08-11. (19/24901-3)

BONALDO, LAUREN M. M.; HURTADO, ELARD J.; MIYAGAKI, OLIMPIO H.. MULTIPLICITY RESULTS FOR ELLIPTIC PROBLEMS INVOLVING NONLOCAL INTEGRODIFFERENTIAL OPERATORS WITHOUT AMBROSETTI-RABINOWITZ CONDITION. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 42, n. 7, p. 25-pg., 2022-03-22. (19/24901-3)

BOER, EDUARDO DE S.; MIYAGAKI, OLIMPIO H.; PUCCI, PATRIZIA. Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential. RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, v. 33, n. 3, p. 25-pg., 2022-01-01. (19/22531-4, 19/24901-3)

BUENO, HAMILTON P.; CAQUI, EDUARDO HUERTO; MIYAGAKI, OLIMPIO H.. Critical fractional elliptic equations with exponential growth. JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, v. 7, n. 1, p. 25-pg., 2021-03-01. (19/24901-3)

BARBOZA, EUDES M.; MIYAGAKI, OLIMPIO H.; PEREIRA, FABIO R.; SANTANA, CLAUDIA R.. HENON EQUATION WITH NOLINEARITIES INVOLVING SOBOLEV CRITICAL GROWTH IN H-0,rad(1)(B-1). Electronic Journal of Differential Equations, v. N/A, p. 18-pg., 2021-03-29. (19/24901-3)