We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden's equation -Δu = |u|3 on an unbounded L-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
A computer-assisted existence proof for Emden’s equation on an unbounded L-shaped domain / Plum, Michael; Ruetters, Dagmar; Pacella, Filomena. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 19:2(2017). [10.1142/S0219199717500055]
A computer-assisted existence proof for Emden’s equation on an unbounded L-shaped domain
Pacella, Filomena
2017
Abstract
We prove existence, non-degeneracy, and exponential decay at infinity of a non-trivial solution to Emden's equation -Δu = |u|3 on an unbounded L-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 solutionFile | Dimensione | Formato | |
---|---|---|---|
Pacella_Computer-assisted-existence_2017.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
630.13 kB
Formato
Adobe PDF
|
630.13 kB | Adobe PDF | Contatta l'autore |
Pacella_preprint_Computer-assisted-existence_2017.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Creative commons
Dimensione
413.8 kB
Formato
Unknown
|
413.8 kB | Unknown |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.