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The critical Choquard-Schrodinger-Poisson problems: radial and nonradial solution, existence and multiplicity

Grant number: 21/08059-0
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): June 01, 2022
Effective date (End): May 31, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Olimpio Hiroshi Miyagaki
Grantee:Eduardo de Souza Böer
Supervisor abroad: Patrizia Pucci
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Research place: Università degli Studi di Perugia, Italy  
Associated to the scholarship:19/22531-4 - Critical non local Choquard-Schrödinger-Poisson equation: existence, multiplicity and properties, BP.DR

Abstract

In this project we will study a class of Schrodinger-Poisson type problems, as well as, Choquard-Schrondiger-Poisson problems, in R^N, if N=2,3. The study in R^2 presents a crucial difficulty, since the equation involves a convolution with the logarithm function. We consider the problems with potentials that permit recover the compactness of the embedding. We will study problems with prescript norm and problems involving the fractional operator with Hardy singular potential, aiming to obtain the existence of radial and nonradial solutions.

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