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

The asymptotic behavior of one-dimensional nonlocal Kirchhoff type bifurcation curves is precisely studied. This problem is motivated by the nonlocal logistic equation of population dynamics investigated recently by the author. We establish the new precise asymptotic formulas for $$L^2$$ bifurcation curves $$\lambda = \lambda (\alpha )$$ as $$\alpha \rightarrow \infty $$ , where $$\alpha := \Vert u_\lambda \Vert _2$$ .