Scholarship 23/09656-8 - Equações diferenciais parciais elíticas, Equações de evolução - BV FAPESP
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A study about elliptical partial differential equations of Choquard type

Grant number: 23/09656-8
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date until: December 01, 2023
End date until: January 31, 2025
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Olimpio Hiroshi Miyagaki
Grantee:Braulio Brendo Vasconcelos Maia
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 present two elliptical Partial Differential Equation problems with a Choquard-type nonlinearity, which is characterized by the convolution between two functions, thus being a nonlocal nonlinearity, that is, it does not depend on the spatial variable. In our case, the first problem we present a Choquard equation related to the Schrodinger-Poisson system, in this case, together with the Choquard term we will have a weight function that changes sign and that is null in a subset of non-zero measure; we will first study an eigenvalue problem associated with this first problem and then use bifurcation results to obtain results of existence and non-existence of solutions. Regarding the second problem, we have a Choquard equation with the presence of the convection term, that is, a non-linearity that depends on the gradient; to guarantee the existence of a solution for this problem, we will study an associated evolution problem so that the solution of such problem converges (with respect to time) to a stationary function that is the solution of the original problem (AU)

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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)
LI, HAOYU; MAIA, BRAULIO B. V.; MIYAGAKI, OLIMPIO H.. Existence of two normalized solutions for a Choquard equation with exponential growth and an L2-subcritical perturbation. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 75, n. 6, p. 19-pg., . (22/16407-1, 23/09656-8, 22/15812-0)
MAIA, BRAULIO B. V.; NOBREGA, ALANNIO B.. Bifurcation results for a class of elliptic equations with a nonlocal reaction term and interior interface boundary conditions. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 82, p. 11-pg., . (23/09149-9, 23/09656-8)

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