Nonlinear Functional Analysis
by Gerald Teschl
Publisher: University of Vienna 2009
Number of pages: 74
This manuscript provides a brief introduction to nonlinear functional analysis. We start out with calculus in Banach spaces, review differentiation and integration, derive the implicit function theorem and apply the result to prove existence and uniqueness of solutions for ordinary differential equations in Banach spaces. Next we introduce the mapping degree in both finite and infinite dimensional Banach spaces.
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