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

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### 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.

### Most cited references15

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### Bifurcation from simple eigenvalues

(1971)
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### Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

(1976)
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### Some global results for nonlinear eigenvalue problems

(1971)
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### Author and article information

###### Journal
2014-08-29
2014-09-14
1409.0070