Open AccessWeighted fourth order elliptic problems in the unit ball
Author(s) -
Guo Zhang,
Fangshu Wan
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021061
Subject(s) - mathematics , unit sphere , uniqueness , sobolev space , ball (mathematics) , dirichlet distribution , combinatorics , order (exchange) , pure mathematics , mathematical analysis , finance , economics , boundary value problem
Existence and uniqueness of positive radial solutions of some weighted fourth order elliptic Navier and Dirichlet problems in the unit ball \begin{document}$ B $\end{document} are studied. The weights can be singular at \begin{document}$ x = 0 \in B $\end{document} . Existence of positive radial solutions of the problems is obtained via variational methods in the weighted Sobolev spaces. To obtain the uniqueness results, we need to know exactly the asymptotic behavior of the solutions at the singular point \begin{document}$ x = 0 $\end{document} .