scholarly journals Uniqueness of positive radial solutions of the Brezis-Nirenberg problem on thin annular domains on \begin{document}$ {\mathbb S}^n $\end{document} and symmetry breaking bifurcations

2020 ◽  
Vol 19 (10) ◽  
pp. 4727-4770
Author(s):  
Naoki Shioji ◽  
◽  
Kohtaro Watanabe ◽  
Keyword(s):  
Symmetry Breaking ◽  
Radial Solutions ◽  
Positive Radial Solutions ◽  
Annular Domains ◽  
Nirenberg Problem

scholarly journals Existence of positive radial solutions for a class of nonlinear singular elliptic problems in annular domains

1992 ◽  
Vol 35 (3) ◽  
pp. 405-418 ◽  
Author(s):  
Zongming Guo
Keyword(s):  
Boundary Conditions ◽  
Degree Theory ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Radial Solutions ◽  
Positive Radial Solutions ◽  
Annular Domains ◽  
Radially Symmetric Solutions

We establish the existence of positive radially symmetric solutions of Δu+f(r,u,u′) = 0 in the domainR1<r<R0with a variety of Dirichlet and Neumann boundary conditions. The functionfis allowed to be singular when eitheru= 0 oru′ = 0. Our analysis is based on Leray-Schauder degree theory.

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