Tetsutaro Shibata
Abstract:
We consider the nonlinear eigenvalue problem
where
are constants and
is a parameter.
It is known in [13] that the bifurcation curve
consists of two branches, which are denoted by
.
Here,
. We establish the
asymptotic behavior of the turning point
of
,
namely, the point which satisfies
as
and
.
We also establish the asymptotic formulas for
and
as
and
,
respectively.
Submitted June 20, 2016. Published July 27, 2016.
Math Subject Classifications: 34F10.
Key Words: Asymptotic behavior; parabola-like bifurcation curves.
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Tetsutaro Shibata Laboratory of Mathematics Institute of Engineering Hiroshima University Higashi-Hiroshima, 739-8527, Japan email: shibata@amath.hiroshima-u.ac.jp |
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