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\[\text{div}\big(\phi_{N}(\nabla v)\big)+\lambda f(|x|, v)=0 \text{in} B(R), v=0 \text{on} \partial B(R), \]where \(\phi_{N}(y)=\frac{y}{\sqrt{1-|y|^{2}}}, y\in \mathbb{R}^{N}\), \(\lambda\) 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.