A reduction algorithm for sublinear Dirichlet problems

J. Cossio, S. Lee, John M Neuberger

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a sublinear elliptic BVP on the unit square and recall proofs for the existence of five solutions. Previous algorithms which follow the constructive nature of the existence proofs are able to find four of these solutions. The fifth solution follows from an application of the Lyapunov-Schmidt reduction method. We provide here a new algorithm for approximating this solution which realizes the reduction minimizing function. We implement this new algorithm using an orthonormal finite sub-basis of eigenfunctions.

Original languageEnglish (US)
Pages (from-to)3379-3390
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume47
Issue number5
DOIs
StatePublished - Aug 2001
Externally publishedYes

Fingerprint

Dirichlet Problem
Lyapunov-Schmidt Method
Lyapunov-Schmidt Reduction
Orthonormal
Reduction Method
Eigenvalues and eigenfunctions
Eigenfunctions
Unit

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)

Cite this

A reduction algorithm for sublinear Dirichlet problems. / Cossio, J.; Lee, S.; Neuberger, John M.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 47, No. 5, 08.2001, p. 3379-3390.

Research output: Contribution to journalArticle

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