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Study of semiclassical solutions to the stationary nonlinear Dirac equation

Grant number: 14/16136-1
Support Opportunities:Regular Research Grants
Duration: January 01, 2015 - December 31, 2016
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 propose studying some questions about existence and concentration of nontrivial solutions to the stationary nonlinear Dirac equation, where this equation describes a model to the Quantum Mechanics which, despite Schrödinger equation, takes into account the Relativistic Theory. We mean to study three issues on this subject by using variational methods. The first one is about the existence of solutions which concentrate around manifolds of R3. The second treats of Dirac equation with singularly potential and the last one deals with this class of problem with asymptotic linear nonlinearities. (AU)

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VEICULO: TITULO (DATA)
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Scientific publications (9)
(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)
PIMENTA, MARCOS TO. Radial sign-changing solutions to biharmonic nonlinear Schrodinger equations. BOUNDARY VALUE PROBLEMS, . (12/20160-0, 14/16136-1)
ALVES, MICHELE O.; PIMENTA, MARCOS T. O.; SUAREZ, ANTONIO. Lotka-Volterra models with fractional diffusion. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. 147, n. 3, p. 505-528, . (14/16136-1)
FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. Existence of ground state solutions to Dirac equations with vanishing potentials at infinity. Journal of Differential Equations, v. 262, n. 1, p. 486-505, . (14/16136-1, 15/12476-5)
PIMENTA, MARCOS TO. Radial sign-changing solutions to biharmonic nonlinear Schrodinger equations. BOUNDARY VALUE PROBLEMS, v. N/A, p. 17-pg., . (12/20160-0, 14/16136-1)
FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A PRESCRIBED MEAN-CURVATURE PROBLEM WITH CRITICAL GROWTH. Electronic Journal of Differential Equations, v. N/A, p. 15-pg., . (14/16136-1)
FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. Nodal solutions of an NLS equation concentrating on lower dimensional spheres. BOUNDARY VALUE PROBLEMS, . (14/16136-1)
FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A PRESCRIBED MEAN-CURVATURE PROBLEM WITH CRITICAL GROWTH. Electronic Journal of Differential Equations, . (14/16136-1)
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, . (14/16136-1, 12/20160-0)
FIGUEIREDO, GIOVANY M.; PIMENTA, MARCOS T. O.. Nodal solutions of an NLS equation concentrating on lower dimensional spheres. BOUNDARY VALUE PROBLEMS, v. N/A, p. 19-pg., . (14/16136-1)

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