scholarly journals Existence of Multiple Positive Radial Solutions for $p$-Laplacian Problems with an L1-Indefinite Weight

2011 ◽  
Vol 15 (2) ◽  
pp. 723-736 ◽  
Author(s):  
Chan-Gyun Kim ◽  
Yong-Hoon Lee
Keyword(s):  
Indefinite Weight ◽  
Radial Solutions ◽  
Positive Radial Solutions

scholarly journals Weighted fourth order elliptic problems in the unit ball

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zongming Guo ◽  
Fangshu Wan
Keyword(s):  
Asymptotic Behavior ◽  
Singular Point ◽  
Unit Ball ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Positive Radial Solutions

<p style='text-indent:20px;'>Existence and uniqueness of positive radial solutions of some weighted fourth order elliptic Navier and Dirichlet problems in the unit ball <inline-formula><tex-math id="M1">\begin{document}$ B $\end{document}</tex-math></inline-formula> are studied. The weights can be singular at <inline-formula><tex-math id="M2">\begin{document}$ x = 0 \in B $\end{document}</tex-math></inline-formula>. Existence of positive radial solutions of the problems is obtained via variational methods in the weighted Sobolev spaces. To obtain the uniqueness results, we need to know exactly the asymptotic behavior of the solutions at the singular point <inline-formula><tex-math id="M3">\begin{document}$ x = 0 $\end{document}</tex-math></inline-formula>.</p>

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