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

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 $λ= λ(α)$ as $α\to \infty$, where $α:= \Vert u_λ\Vert_2$.

💡 Research Summary

The paper investigates a one‑dimensional nonlocal Kirchhoff‑type elliptic problem that originates from a logistic equation in population dynamics. The governing equation is

\