Bifurcation curves of a Dirichlet problem with geometrically concave nonlinearity and an application to the generalized logistic growth model

Hung, Kuo-Chih

doi:10.1090/proc/15274

Bifurcation curves of a Dirichlet problem with geometrically concave nonlinearity and an application to the generalized logistic growth model
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Proc. Amer. Math. Soc. 149 (2021), 1117-1126 Request permission

Abstract:

We study the bifurcation curves for a Dirichlet problem with geometrically concave nonlinearity. We give an application to the generalized logistic growth model \begin{equation*} \left \{ \begin {array}{l} u^{\prime \prime }(x)+\lambda f(u)=0\text {,}\;-1<x<1\text {, \ }u(-1)=u(1)=0 \text {,} \\ f(u)=u^{\alpha }\left [ 1-\left ( \frac {u}{K}\right ) ^{\beta }\right ] ^{\gamma }\text {, }\alpha ,\beta ,\gamma >0\text {.}\end{array}\right . \end{equation*} There are totally six qualitatively bifurcation curves of order relations for $(\alpha ,\beta ,\gamma )$.

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