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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.

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      Most cited references 15

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      Bifurcation from simple eigenvalues

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        Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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          Some global results for nonlinear eigenvalue problems

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            Author and article information

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

            http://creativecommons.org/licenses/by/3.0/

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            math.AP

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