Local and Global Inversion Theorems

  • Antonio Ambrosetti
  • David Arcoya
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 82)


This chapter deals with the local inversion theorem and the implicit function theorem in Banach spaces. The Lyapunov—Schmidt reduction is discussed in Section 3.3. In Section 3.4 we prove the global inversion theorem, which goes back to Hadamard and Caccioppoli. Section 3.5 deals with a global inversion theorem in the presence of fold singularities.


Banach Space Unique Solution Neighborhood Versus Implicit Function Theorem Auxiliary Equation 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.SISSA-International School for Advanced StudiesTriesteItaly
  2. 2.Departamento de Análisis MatemáticoUniversidad de GranadaGranadaSpain

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