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Tohoku Mathematical Journal
SECOND SERIES VOL. 61, NO. 2
|Tohoku Math. J.|
61 (2009), 287-307
THE STRUCTURE OF RADIAL SOLUTIONS FOR ELLIPTIC EQUATIONS ARISING FROM THE SPHERICAL ONSAGER VORTEX
Zhi-You Chen, Jann-Long Chern and Yong-Li Tang
(Received May 2, 2008, revised January 9, 2009)
In this paper, we consider a nonlinear elliptic equation on the plane away from the origin, which arises from the spherical Onsager vortex theory in physics or the problem of prescribing Gaussian curvature in geometry. Depending on various situations for the prescribed function in the nonlinear term, the complete structure of radial solutions in terms of initial data will be offered.
2000 Mathematics Subject Classification.
Primary 35J60; Secondary 35B05.
Key words and phrases.
Elliptic equation, spherical Onsager vortex, structure of solutions.
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