Yu-Hao Liang, Shin-Hwa Wang
Abstract:
In this article, we study the classification and evolution of bifurcation curves
of positive solutions for the one-dimensional perturbed Gelfand equation with
mixed boundary conditions,
where
.
We prove that, for
,
there exist two nonnegative
satisfying
for
,
and
for
,
such that, on the
-plane,
(i) when
,
the bifurcation curve is strictly increasing;
(ii) when
,
the bifurcation curve is monotone increasing;
(iii) when
,
the bifurcation curve is S-shaped;
(iv) when
,
the bifurcation curve is C-shaped. This work
is a continuation of the work by Liang and Wang [8] where
authors studied this problem for
,
and our results partially
prove a conjecture on this problem for
in [8].
Submitted November 30, 2016. Published February 28, 2017.
Math Subject Classifications: 34B18, 74G35.
Key Words: Multiplicity; positive solution; perturbed Gelfand equation;
S-shaped bifurcation curve; C-shaped bifurcation curve; time map.
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Yu-Hao Liang Department of Applied Mathematics National Chiao Tung University Hsinchu 300, Taiwan email: yhliang@nctu.edu.tw | |
Shin-Hwa Wang Department of Mathematics National Tsing Hua University Hsinchu 300, Taiwan email: shwang@math.nthu.edu.tw |
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