Gianni Arioli, Hans Koch
Validated numerical solutions for a semilinear elliptic equation 
on some topological annuli in the plane
(6421K, pdf)

ABSTRACT.  We consider the equation -Laplace w = w^3 with zero boundary conditions 
on planar domains that are conformal images of annuli. 
Starting with an approximate solution, 
we prove that there exist a true solution nearby. 
Our approach is computer-assisted. 
It involves simultaneous and accurate control of 
the (inverse) Dirichlet Laplacean, nonlinearities, and conformal mappings.