Asymptotic behavior of bifurcation curves of nonlocal logistic equation of population dynamics

We study the one-dimensional nonlocal Kirchhoff type bifurcation problem related to logistic equation of population dynamics. We establish the precise asymptotic formulas for bifurcation curve $\lambda = \lambda (\alpha )$ as $\alpha \to \infty $ in $L^{2}$-framework, where $\alpha := \Vert u_{\lambda }\Vert _{2}$.