English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove existence, non-degeneracy, and exponential decay at infinity of anon-trivial solution to Emden's equation $-\Delta u = | u |^3$ on an unbounded$L$-shaped domain, subject to Dirichlet boundary conditions. Besides the directvalue of this result, we also regard this solution as a building block forsolutions on expanding bounded domains with corners, to be established infuture work. Our proof makes heavy use of computer assistance: Starting from anumerical approximate solution, we use a fixed-point argument to proveexistence of a near-by exact solution. The eigenvalue bounds established in thecourse of this proof also imply non-degeneracy of the solution.

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