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.
|Number of pages
|Nonlinear Analysis, Theory, Methods and Applications
|Published - Aug 2001
ASJC Scopus subject areas
- Applied Mathematics