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International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 10, Pages 605-613
http://dx.doi.org/10.1155/S0161171201003544

Boundary value problem for r2d2f/dr2+f=f3 (I): existence and uniqueness

1Department of Mathematics, University of Pittsburgh, Pittsburgh 15260, PA, USA
2Department of Mathematics, University of California, Davis 95616, CA, USA

Received 16 June 1999

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the equation r2d2f/dr2+f=f3 with the boundary conditions f(1)=0, f()=1, and f(r)>0 for 1<r<. The existence of the solution is proved using a topological shooting argument. And the uniqueness is proved by a variation method.