Open AccessSingular weighted sharp Trudinger-Moser inequalities defined on $ \mathbb{R}^N $ and applications to elliptic nonlinear equations
Author(s) -
Sami Aouaoui,
Rahma Jlel
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021137
Subject(s) - mathematics , type (biology) , euclidean space , nonlinear system , pure mathematics , compact space , logarithm , singularity , infinity , euclidean geometry , mathematical analysis , geometry , physics , ecology , quantum mechanics , biology
This work comes to complete some previous ones of ours. Actually, in this paper, we establish some singular weighted inequalities of Trudinger-Moser type for radial functions defined on the whole euclidean space \begin{document}$ \mathbb{R}^N,\ N \geq 2. $\end{document} The weights considered are of logarithmic type. The singularity plays a capital role to prove the sharpness of the inequalities. These inequalities are later improved using some concentration-compactness arguments. The last part in this work is devoted to the application of the inequalities established to some singular elliptic nonlinear equations involving a new growth conditions at infinity of exponential type.