Asymptotic formulas for $L^2$ bifurcation curves of nonlocal logistic equation of population dynamics

Abstract

The one-dimensional nonlocal Kirchhoff type bifurcation problems which are derived from logistic equation of population dynamics are studied. We obtain the precise asymptotic shapes of $L^2$ bifurcation curves $\lambda = \lambda(\alpha)$ as $\alpha \to \infty$, where $\alpha:= \Vert u_\lambda \Vert_2$.