Abstract
In this paper, we study the uniqueness and multiplicity of positive solutions of one-dimensional prescribed mean curvature equation $ \left\{ \begin{array}{l} - \left({\frac{{u'}}{{\sqrt {1 - u{'^2}} }}} \right)' = \lambda f\left(u \right), u\left(x \right) \gt 0, - 1 \lt x \lt 1, u\left({ - 1} \right) = u\left(1 \right) = 0, \end{array} \right. $ where $\lambda$ is a positive parameter. The main tool is the fixed point index in cones.
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