Boundary value problem for r2d2f/dr2+f=f3 (I): existence and uniqueness - Chie Bing Wang (International Journal of Mathematics and Mathematical Sciences)
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.