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Zeitschrift für Analysis und ihre Anwendungen

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Volume 5, Issue 6, 1986, pp. 491–506
DOI: 10.4171/ZAA/218

Published online: 1986-12-31

Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen

Matthias Günther[1]

(1) Universität Leipzig, Germany

The solvability of the nonlinear implicit equation $F(u,f) = 0$ in Banach spaces is examined. Theorem 1 covers situations in which $D_uF^{-1}$ does not exist, but $F$ can be approximated by means of mappings $F_t$ with better properties. Theorem 2 is of Moser-Nash type. In order to obtain optimal regularity results the Newton iteration method is combined with a triple approximation technique using smoothing operators and properties of certain interpolation spaces.

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Günther Matthias: Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen. Z. Anal. Anwend. 5 (1986), 491-506. doi: 10.4171/ZAA/218