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
• City of the host institution: São Carlos
• 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

(28)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

ALVES, CLAUDIANOR O.; JI, CHAO; MIYAGAKI, OLIMPIO H.. Multiplicity of normalized solutions for a nonlinear Schrodinger equation with critical growth in ℝ^N. ANALYSIS AND APPLICATIONS, v. N/A, p. 21-pg., 2025-09-06. (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)

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)

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)

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)

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)

DE PAIVA, FRANCISCO O.; MIYAGAKI, OLIMPIO H.; PRESOTO, ADILSON E.. EXISTENCE OF SOLUTIONS FOR THE BREZIS-NIRENBERG PROBLEM. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 61, n. 2, p. 9-pg., 2023-06-01. (19/24901-3, 17/16108-6)

BUENO, H. P.; MIYAGAKI, O. H.; VIEIRA, A. L.. Multiplicity of solutions for a scalar field equation involving a fractional p-Laplacian with general nonlinearity. Complex Variables and Elliptic Equations, v. 69, n. 12, p. 24-pg., 2023-11-14. (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)

CARDOSO, M.; DE OLIVEIRA, J. F.; MIYAGAKI, O. H.. Normalized solutions for INLS equation with critical Hardy-Sobolev type nonlinearities. Journal of Fixed Point Theory and Applications, v. 27, n. 3, p. 26-pg., 2025-08-09. (19/24901-3)

GONCALVES, J. V.; MARCIAL, M. R.; MIYAGAKI, O. H.; DOS SANTOS, C. A. P.. Topological structure of the set of solution for singular elliptic equations with a convective term. Journal of Mathematical Analysis and Applications, v. 552, n. 2, p. 26-pg., 2025-12-15. (19/24901-3)

BOER, EDUARDO DE S.; MIYAGAKI, OLIMPIO H.. THE CHOQUARD LOGARITHMIC EQUATION INVOLVING A NONLINEARITY WITH EXPONENTIAL GROWTH. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 60, n. 1, p. 23-pg., 2022-09-01. (19/24901-3, 19/22531-4)

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)