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

TL;DR

This paper derives precise asymptotic formulas for solutions of a one-dimensional Kirchhoff type elliptic equation with a logarithmic Kirchhoff function as the bifurcation parameter grows large.

Contribution

It provides the first detailed asymptotic analysis of solutions to Kirchhoff equations with logarithmic functions as the parameter tends to infinity.

Findings

Established asymptotic formulas for solutions as λ→∞

Identified the behavior of solutions in the large parameter limit

Contributed to understanding nonlocal elliptic equations with logarithmic Kirchhoff functions

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.