A reduction algorithm for sublinear Dirichlet problems

J. Cossio; S. Lee; J. M. Neuberger

doi:10.1016/S0362-546X(01)00453-9

A reduction algorithm for sublinear Dirichlet problems

J. Cossio, S. Lee, J. M. Neuberger

Mathematics and Statistics

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3 Scopus citations

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 language	English (US)
Pages (from-to)	3379-3390
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	47
Issue number	5
DOIs	https://doi.org/10.1016/S0362-546X(01)00453-9
State	Published - Aug 2001

ASJC Scopus subject areas

Analysis
Applied Mathematics

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AU - Neuberger, J. M.

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AB - 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.

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A reduction algorithm for sublinear Dirichlet problems

Abstract

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