Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 10, pp. 1-12.

Title: Complete classification of bifurcation curves for a multiparameter diffusive logistic
       problem with generalized Holling type-IV functional response
       
Authors: Jyun-Yuan Ciou (National Univ. of Tainan, Taiwan)
         Tzung-Shin Yeh (National Univ. of Tainan, Taiwan)

Abstract:
 We study exact multiplicity and bifurcation curves of positive solutions for
 the diffusive logistic problem with generalized Holling type-IV functional
 response
 $$\displaylines{
 u''(x)+\lambda \big[ ru(1-\frac{u}{q})-\frac{u}{1+mu+u^2}\big] =0,\quad-1<x<1, \cr
 u(-1)=u(1)=0,
 }$$
 where the quantity in brackets is the growth rate function
 and $\lambda >0$ is a bifurcation parameter. On the
 $(\lambda ,||u||_{\infty })$-plane, we give a complete classification of
 two qualitatively different bifurcation curves: a C-shaped curve
 and a monotone increasing curve.

Submitted April 5, 2019. Published February 23, 2021.
Math Subject Classifications: 34B15, 34B18.
Key Words: Bifurcation curve; exact multiplicity; diffusive logistic problem;
           Holling type-IV functional response; time map.