## Bifurcation without Frechet differentiability at the trivial solution

Criteria for the bifurcation of small solutions of an equation F(lambda,u) = 0 from a line {(lambda,0): lambda is an element of R} of trivial solutions are usually based on properties of the DuF(lambda,0) at the trivial solutions, where the partial derivative is taken in the sense of Frechet. When this derivative only exists in some weaker sense, the situation charges considerably and much remains to be carried out to understand the conditions under which bifurcation takes place. This paper summarizes and extends one direction of research in this direction, where only Hadamard differentiability is required. In addition to presenting the abstract results, their application to the study of bound states of a class of nonlinear elliptic equations on R-N is also examined. Copyright (c) 2015 John Wiley & Sons, Ltd.

Publié dans:
Mathematical Methods In The Applied Sciences, 38, 16, 3444-3463
Année
2015
Publisher:
Hoboken, Wiley-Blackwell
ISSN:
0170-4214
Mots-clefs:
Laboratoires:

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Notice créée le 2016-02-16, modifiée le 2018-12-03

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