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

Abstract

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 $\lambda \to \infty$. Here, $\lambda >0$ is the bifurcation parameter.