Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane
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 (inve...
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| Published in: | Journal of Differential Equations Vol. 353; pp. 420 - 436 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
25-04-2023
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| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2023.02.013 |