Elliptic problems by variational and topological methods

• Grant number: 17/16108-6
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2017
• End date: October 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Francisco Odair Vieira de Paiva
• Grantee: Francisco Odair Vieira de Paiva
• 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: Adilson Eduardo Presoto ; Lynnyngs Kelly Arruda Saraiva de Paiva

Abstract

The central theme of this project is to study the existence and multiplicity of solutions for some classes of nonlinear elliptic problems, originated in the mathematical-physics. To solve these problems, we propose to combine variational and topological techniques; and techniques from the study of differential equations: sub-super solutions, a-priori estimates, Nehari manifold, among others. The proposed problems are based on papers that we published in recent years. As is natural in mathematical research, many questions related to possible generalizations of the results are open. Thus, we intend to try to answer these questions. (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)

ARCOYA, DAVID; DE PAIVA, FRANCISCO ODAIR; MENDOZA, JOSE M.. Existence of solutions for a nonhomogeneous elliptic Kircchoff type equation. Journal of Mathematical Analysis and Applications, v. 480, n. 2, DEC 15 2019. (17/16108-6, 18/12881-5)

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; 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)

FERREIRA, FABIANA MARIA; DE PAIVA, FRANCISCO ODAIR. ON A RESONANT AND SUPERLINEAR ELLIPTIC SYSTEM. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 39, n. 10, p. 5775-5784, OCT 2019. (17/16108-6)

ARCOYA, DAVID; DE PAIVA, FRANCISCO ODAIR; MENDOZA, JOSE M.. Existence of solutions for a nonhomogeneous semilinear elliptic equation. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 195, JUN 2020. (17/16108-6, 18/12881-5)

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)