A Pohožaev type identity and its application to uniqueness of positive radial solutions of Brezis-Nirenberg problem on an annulus

2021 ◽  
Vol 497 (2) ◽  
pp. 124901
Author(s):  
Naoki Shioji ◽  
Kohtaro Watanabe
Keyword(s):  
Radial Solutions ◽  
Type Identity ◽  
Positive Radial Solutions ◽  
Pohozaev Type Identity ◽  
Nirenberg Problem

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>

Positive radial solutions for p-Laplacian systems

2008 ◽  
Vol 75 (1-2) ◽  
pp. 43-50 ◽  
Author(s):  
Donal O’Regan ◽  
Haiyan Wang
Keyword(s):  
Radial Solutions ◽  
Positive Radial Solutions
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