Solutions for elliptic problems

• Grant number: 15/11912-6
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2015
• End date: August 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Rodrigo da Silva Rodrigues
• Grantee: Rodrigo da Silva Rodrigues
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this project we will study the existence of solutions for elliptic problems with nonlinearities of subcritical and critical growth. We will give special attention to elliptical problems of Kirchhoff type.So far, by studying some papers developed by some authors, we were able to apply variational and nonvariational methods for a class of problem of Kirchhoff type and we proved some results about the existence of multiple solutions, which improve some of the results of the studied papers. In addition, we believe it is possible to obtain new results, answering some questions still open, thus improving the mathematical knowledge about these kinds of problems. (AU)

Scientific publications

(7)

(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)

HURTADO, ELARD JUAREZ; MIYAGAKI, OLIMPIO HIROSHI; RODRIGUES, RODRIGO DA SILVA. Existence and Asymptotic Behaviour for a Kirchhoff Type Equation With Variable Critical Growth Exponent. Milan Journal of Mathematics, v. 85, n. 1, p. 71-102, JUN 2017. (15/11912-6)

JUAREZ HURTADO, E.; MIYAGAKI, O. H.; RODRIGUES, R. S.. Existence and Multiplicity of Solutions for a Class of Elliptic Equations Without Ambrosetti-Rabinowitz Type Conditions. Journal of Dynamics and Differential Equations, v. 30, n. 2, p. 405-432, JUN 2018. (15/11912-6)

GUIMARAES, MATEUS BALBINO; RODRIGUES, RODRIGO DA SILVA. EXISTENCE OF SOLUTIONS FOR KIRCHHOFF EQUATIONS INVOLVING p-LINEAR AND p-SUPERLINEAR THERMS AND WITH CRITICAL GROWTH. Electronic Journal of Differential Equations, v. N/A, p. 14-pg., 2016-05-03. (15/11912-6)

HURTADO, ELARD JUAREZ; MIYAGAKI, OLIMPIO H.; RODRIGUES, RODRIGO S.. Multiplicity of solutions to class of nonlocal elliptic problems with critical exponents. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, DEC 2021. (15/11912-6)

GUIMARAES, MATEUS BALBINO; HURTADO, ELARD JUAREZ; RODRIGUES, RODRIGO DA SILVA. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NON-DEGENERATE KIRCHHOFF TYPE PROBLEM WITH NONLINEAR BOUNDARY CONDITION. Electronic Journal of Differential Equations, MAR 22 2019. (15/11912-6)

GUIMARAES, MATEUS BALBINO; RODRIGUES, RODRIGO DA SILVA. EXISTENCE OF SOLUTIONS FOR KIRCHHOFF EQUATIONS INVOLVING p-LINEAR AND p-SUPERLINEAR THERMS AND WITH CRITICAL GROWTH. Electronic Journal of Differential Equations, MAY 3 2016. (15/11912-6)

GUIMARAES, MATEUS BALBINO; HURTADO, ELARD JUAREZ; RODRIGUES, RODRIGO DA SILVA. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NON-DEGENERATE KIRCHHOFF TYPE PROBLEM WITH NONLINEAR BOUNDARY CONDITION. Electronic Journal of Differential Equations, v. N/A, p. 12-pg., 2019-03-22. (15/11912-6)