Open AccessQuantitative analysis of a system of integral equations with weight on the upper half space
Author(s) -
Sufang Tang,
Jingbo Dou
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021171
Subject(s) - infinity , mathematics , sobolev space , space (punctuation) , upper and lower bounds , class (philosophy) , pure mathematics , mathematical analysis , artificial intelligence , computer science , philosophy , linguistics
In this paper we analyzed the integrability and asymptotic behavior of the positive solutions to the Euler-Lagrange system associated with a class of weighted Hardy-Littlewood-Sobolev inequality on the upper half space \begin{document}$ \mathbb{R}_+^n. $\end{document} We first obtained the optimal integrability for the solutions by the regularity lifting theorem. And then, with this integrability, we investigated the growth rate of the solutions around the origin and the decay rate near infinity.