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Global bifurcation at isolated singular points of the Hadamard derivative.

作者信息

Stuart C A

机构信息

Section de mathématiques Station 8, EPFL, Lausanne, CH 1015, Switzerland.

出版信息

Philos Trans A Math Phys Eng Sci. 2021 Feb 22;379(2191):20190379. doi: 10.1098/rsta.2019.0379. Epub 2021 Jan 4.

DOI:10.1098/rsta.2019.0379
PMID:33390077
Abstract

Consider [Formula: see text] such that (, 0) = 0 for all [Formula: see text], where and are Banach spaces. Bifurcation from the line [Formula: see text] of trivial solutions is investigated in cases where (, · ) need not be Fréchet differentiable at 0. The main results provide sufficient conditions for to be a bifurcation point and yield global information about the connected component of [Formula: see text] containing (, 0). Some necessary conditions for bifurcation are also formulated. The abstract results are used to treat several singular boundary value problems for which Fréchet differentiability is not available. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.

摘要

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