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Critical non local Choquard-Schrödinger-Poisson equation: existence, multiplicity and properties

Grant number: 19/22531-4
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): June 01, 2020
Effective date (End): February 28, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Olimpio Hiroshi Miyagaki
Grantee:Eduardo de Souza Böer
Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Associated scholarship(s):21/08059-0 - The critical Choquard-Schrodinger-Poisson problems: radial and nonradial solution, existence and multiplicity, BE.EP.DR


In this project we study a class of Schröodinger-Poisson type problem, as well as, Choquard-Schröndiger-Poisson equation, planar and in higher dimensions. The study in planar presents a hardy difficullty, because the equation envolves a convolution of a function with logarithm. We are going to study in higher dimensions, some problems permit to recover the compactness, as well in plane.We will attack some problems with prescribed norm, argument due to Jeanjean, which can help in recover the compactness. We also deal with some problem involving the fractional operator and p-laplacian operator. (AU)

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