| Title: | Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane |
| Authors: | G. Arioli, H. Koch |
| Abstract: | We consider the equation -Δw=w3 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. |
| Paper: | Preprint and program text |
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