On Lipschitz conditions for ordinary differential equations in Fréchet spaces

Gerd Herzog

Displaying similar documents to “On Lipschitz conditions for ordinary differential equations in Fréchet spaces”

Nonuniqueness results for ordinary differential equations

Josef Kalas (1998)

Czechoslovak Mathematical Journal

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In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.

On Lipschitz mappings between Fréchet spaces

P. Mankiewicz (1972)

Studia Mathematica

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A Note on Differentiability of Lipschitz Maps

Rafał Górak (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.

Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions

Luděk Zajíček (2014)

Commentationes Mathematicae Universitatis Carolinae

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We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on $Γ$ -almost everywhere Fréchet differentiability of Lipschitz functions on $c_{0}$ (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at $Γ$ -almost every $x$ at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are $Γ$ -almost everywhere Fréchet...

On the differentiability of Lipschitz mappings in Fréchet spaces

P. Mankiewicz (1973)

Studia Mathematica

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