Affiliation:
1. Section de mathématiques Station 8, EPFL, Lausanne, CH 1015, Switzerland
Abstract
Consider
F
∈
C
(
R
×
X
,
Y
)
such that
F
(
λ
, 0) = 0 for all
λ
∈
R
, where
X
and
Y
are Banach spaces. Bifurcation from the line
R
×
{
0
}
of trivial solutions is investigated in cases where
F
(
λ
, · ) need not be Fréchet differentiable at 0. The main results provide sufficient conditions for
μ
to be a bifurcation point and yield global information about the connected component of
{
(
λ
,
u
)
:
F
(
λ
,
u
)
=
0
and
u
≠
0
}
∪
{
(
μ
,
0
)
}
containing (
μ
, 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’.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
1 articles.
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