Global structure of radial positive solutions for a prescribed mean curvature problem in a ball

Abstract

In this paper, we are concerned with the global structure of radial positive solutions of boundary value problem$$\text{div}({\varphi }_N(\nabla v))+\lambda f(|x|,v)=0\text{in}B(R),v=0\text{on}\partial B(R),$$where ${\varphi }_N(y)=\frac{y}{\sqrt{1-|y{|}^2}},y\in {\mathbb{R}}^N$, $\lambda$ is a positive parameter, $B(R)=\{x\in {\mathbb{R}}^N:|x|<R\}$, and $|\cdot |$ denote the Euclidean norm in ${\mathbb{R}}^N$. All results, depending on the behavior of nonlinear term $f$ near 0, are obtained by using global bifurcation techniques.