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A Numerical Algorithm for Ambrosetti–Prodi Type Operators

  • José Teixeira Cal Neto
  • Carlos Tomei

Abstract

We consider the numerical solution of the equation −Δuf(u)=g, for the unknown u satisfying Dirichlet conditions in a bounded domain Ω. The nonlinearity f has bounded, continuous derivative. The algorithm uses the finite element method combined with a global Lyapunov–Schmidt decomposition.

Keywords

Semilinear elliptic equations Finite element method Lyapunov–Schmidt decomposition 

Notes

Acknowledgements

The results are part of the PhD thesis of the first author [14]. Complete proofs are presented elsewhere. The authors are grateful to CAPES, CNPq, and Faperj for support.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.DMEUNIRIORio de JaneiroBrazil
  2. 2.Departamento de MatemáticaPUC-RioRio de JaneiroBrazil

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