Planar Choquard equations with critical exponential reaction and Neumann boundary condition

Rawat, Sushmita; Radulescu, Vicentiu; Sreenadh, Konijeti

Planar Choquard equations with critical exponential reaction and Neumann boundary condition

Files

MathematischeNachrichten2024Rawat.pdf(287.75 KB)

Date

2024-10-26

Authors

Rawat, Sushmita

Radulescu, Vicentiu

Sreenadh, Konijeti

ORCID

0000-0003-4615-5537

Publisher

Wiley

Altmetrics

Abstract

We study the existence of positive weak solutions for the following problem: (Formula presented.) where (Formula presented.) is a bounded domain in (Formula presented.) with smooth boundary, (Formula presented.) is a bounded measurable function on (Formula presented.), (Formula presented.) is nonnegative real number, (Formula presented.) is the unit outer normal to (Formula presented.), (Formula presented.), and (Formula presented.). The functions (Formula presented.) and (Formula presented.) have critical exponential growth, while (Formula presented.) and (Formula presented.) are their primitives. The proofs combine the constrained minimization method with energy methods and topological tools.

Keywords

Cherrier inequality, Hardy–Littlewood–Sobolev inequality, Moser–Trudinger inequality, Nehari manifold, Neumann problem

Citation

Mathematische Nachrichten. 2024, vol. 297, issue 10, p. 3847-3869.
https://onlinelibrary.wiley.com/doi/full/10.1002/mana.202400095

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/