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

In this paper, we are concerned with the global structure of radial positive solutions of boundary value problem$$\text{div}({\varphi }_N(\mathrm{\nabla }v))+\lambda f(\mathrm{\mid }x\mathrm{\mid },v)=0\text{in}B(R),v=0\text{on}\mathrm{\partial }B(R),$$where ${\varphi }_N(y)=\frac{y}{\sqrt{1-\mathrm{\mid }y{\mathrm{\mid }}^2}},y\in {\mathbb{R}}^N$, $\lambda$ is a positive parameter, $B(R)=\{x\in {\mathbb{R}}^N:\mathrm{\mid }x\mathrm{\mid }<R\}$, and $\mathrm{\mid }\cdot \mathrm{\mid }$ 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.