Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024788 | Nonlinear Analysis: Theory, Methods & Applications | 2016 | 24 Pages |
Abstract
We study the classification and evolution of bifurcation curves of positive solutions u  for the one-dimensional prescribed curvature problem{â(uâ²(x)1+(uâ²(x))2)â²=λexp(aua+u),âL0  is a bifurcation parameter, and L,a>0  are two evolution parameters. We prove that, on (λ,âuââ)-plane, for 036/17, the bifurcation curve is â-shaped or reversed ε-like shaped. In particular, for a>aâââ4.107, the bifurcation curve is (i) â-shaped if L>0 small enough and (ii) reversed ε-like shaped if L  is large enough.
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Authors
Yan-Hsiou Cheng, Kuo-Chih Hung, Shin-Hwa Wang,