Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems

We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems { − [ φ ( u ′ ) ] ′ = λ u p ( 1 − u N ) in ( − L , L ) , u ( − L ) = u ( L ) = 0 , where p > 1, N > 0, λ > 0 is a bifurcation parameter, L > 0 is an evolution parameter, and ϕ (...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2023-12, Vol.73 (4), p.1081-1098
Main Authors: Huang, Shao-Yuan, Hsieh, Ping-Han
Format: Article
Language:English
Subjects:
Analysis
Bifurcations
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Parameters
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Summary:We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems { − [ φ ( u ′ ) ] ′ = λ u p ( 1 − u N ) in ( − L , L ) , u ( − L ) = u ( L ) = 0 , where p > 1, N > 0, λ > 0 is a bifurcation parameter, L > 0 is an evolution parameter, and ϕ ( u ) is either ϕ ( u ) = u or φ ( u ) = u / 1 − u 2 . We prove that the corresponding bifurcation curve is ⊂-shape. Thus, the exact multiplicity of positive solutions can be obtained.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2023.0359-22