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

Shao-Yuan Huang, Ping-Han Hsieh (2023)

Czechoslovak Mathematical Journal

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.

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