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

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

Chie Bing Wang1,2

 1Department of Mathematics, University of Pittsburgh, Pittsburgh 15260, PA, USA
2Department of Mathematics, University of California, Davis 95616, CA, USA
Received 16 June 1999

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.