Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 117, pp. 114.
Direct and inverse bifurcation problems for nonautonomous
logistic equations
Tetsutaro Shibata
Abstract:
We consider the semilinear eigenvalue problem
where p > 1 is a constant,
and
is a parameter. We propose a new
inverse bifurcation problem. Assume that k(t) is an unknown
function. Then can we determine k(t) from the asymptotic behavior of
the bifurcation curve?
The purpose of this paper is to answer this question affirmatively.
The key ingredient is the precise asymptotic formula for
the
bifurcation curve
as
(
),
where
.
Submitted December 28, 2012. Published May 10, 2013.
Math Subject Classifications: 34C23, 34B15.
Key Words: Inverse bifurcation problem; nonautonomous equation;
logistic equations.
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Tetsutaro Shibata
Laboratory of Mathematics, Institute of Engineering
Hiroshima University, HigashiHiroshima, 7398527, Japan
email: shibata@amath.hiroshimau.ac.jp

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