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

Abstract

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 $\alpha :=\Vert u_{\lambda }{\Vert }_2$.