Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane
Gianni Arioli, Hans Koch · Journal of Differential Equations · 2023
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 exists a true solution nearby. Our approach is computer-assisted. It involves simultaneous and accurate control of the (inverse) Dirichlet Laplacean, nonlinearities, and conformal mappings.