Asymptotics of solution curves of Kirchhoff type elliptic equations with logarithmic Kirchhoff function

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with logarithmic Kirchhoff function. We establish the precise asymptotic formulas for the solution $u_{\lambda }(x)$ as $\lambda \to \mathrm{\infty }$. Here, $\lambda >0$ is the bifurcation parameter.