A bifurcation analysis on a nonlocal overdetermined problem

TL;DR

This paper investigates a nonlocal overdetermined problem with Kirchhoff type terms, analyzing solution bifurcations and asymptotic behaviors related to the bifurcation parameter, extending classical results by Serrin.

Contribution

It provides a detailed bifurcation analysis for a nonlocal Kirchhoff problem, including solution counts and asymptotic behaviors, which is a novel extension of classical overdetermined problems.

Findings

Number of solutions varies with the bifurcation parameter.

Bifurcation curves exhibit specific asymptotic behaviors for large parameters.

The analysis extends classical results to nonlocal Kirchhoff problems.

Abstract

In this paper, we study an overdetermined problem with Kirchhoff type nonlocal terms related to the celebrated work by Serrin. We obtain the precise number of solutions according to the value of the bifurcation parameter and study asymptotics of bifurcation curves of solutions when the bifurcation parameter is large in some cases.