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

By Ruyun Ma, Hongliang Gao, Yanqiong Lu. 2014

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4499101a4fe689f08e9cc5efc5fe4458f7fbe685