Electron. J. Differential Equations,
Vol. 2017 (2017), No. 61, pp. 112.
Classification and evolution of bifurcation curves for the onedimensional
perturbed Gelfand equation with mixed boundary conditions II
YuHao Liang, ShinHwa Wang
Abstract:
In this article, we study the classification and evolution of bifurcation curves
of positive solutions for the onedimensional 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 Sshaped;
(iv) when
,
the bifurcation curve is Cshaped. 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;
Sshaped bifurcation curve; Cshaped bifurcation curve; time map.
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YuHao Liang
Department of Applied Mathematics
National Chiao Tung University
Hsinchu 300, Taiwan
email: yhliang@nctu.edu.tw


ShinHwa Wang
Department of Mathematics
National Tsing Hua University
Hsinchu 300, Taiwan
email: shwang@math.nthu.edu.tw

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