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A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain
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
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