Existence, non-existence and concentration of solutions to some biharmonic problems and systems

• Grant number: 12/20160-0
• Support Opportunities: Regular Research Grants
• Duration: January 01, 2013 - December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Marcos Tadeu de Oliveira Pimenta
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project the author proposes the study of some questions about existence and concentration of solutions to some elliptic partial differential equations involving the biharmonic operator. More specifically, its proposed the study of three problems, in which in two of them the concern is about a stationary version of the Schrödinger biharmonic equation. The first one deals with some questions about the existence of nontrivial solutions, assuming in the nonlinearity f a critical exponential growth condition. In the second one, its proposed the study of at least three nontrivial solutions, including a nodal (sign-changing solution) one. In the last problem, its proposed the study of some results about the well known Lane-Emden conjecture, in which the concern is about nonexistence results to the Lane-Emden system to some specific values of the exponents p and q. (AU)

Scientific publications

(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)

DELGADO, MANUEL; FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.; SUAREZ, ANTONIO. STUDY OF A LOGISTIC EQUATION WITH LOCAL AND NON-LOCAL REACTION TERMS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 47, n. 2, p. 693-713, JUN 2016. (14/16136-1, 12/20160-0)

PIMENTA, MARCOS TO. Radial sign-changing solutions to biharmonic nonlinear Schrodinger equations. BOUNDARY VALUE PROBLEMS, JAN 31 2015. (12/20160-0, 14/16136-1)

PIMENTA, MARCOS TO. Radial sign-changing solutions to biharmonic nonlinear Schrodinger equations. BOUNDARY VALUE PROBLEMS, v. N/A, p. 17-pg., 2015-01-31. (12/20160-0, 14/16136-1)