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