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- Title
A computer-assisted existence proof for Emden's equation on an unbounded -shaped domain.
- Authors
Pacella, Filomena; Plum, Michael; Rütters, Dagmar
- Abstract
We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden's equation on an unbounded -shaped domain, subject to Dirichlet boundary conditions. Besides the direct value of this result, we also regard this solution as a building block for solutions on expanding bounded domains with corners, to be established in future work. Our proof makes heavy use of computer assistance. Starting from a numerical approximate solution, we use a fixed-point argument to prove existence of a near-by exact solution. The eigenvalue bounds established in the course of this proof also imply non-degeneracy of the solution.
- Subjects
LANE-Emden equation; NON-degenerate perturbation theory; EXPONENTIAL decay law; DIRICHLET forms; COMPUTER assisted instruction
- Publication
Communications in Contemporary Mathematics, 2017, Vol 19, Issue 2, p-1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199717500055