Local and Global Inversion Theorems
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.
KeywordsBanach Space Unique Solution Neighborhood Versus Implicit Function Theorem Auxiliary Equation
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