Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space
In this paper, we study the uniqueness and multiplicity of positive solutions of one-dimensional prescribed mean curvature equation \begin{equation*}\left\{ \begin{array}{l} - \left({\frac{{u'}}{{\sqrt {1 - u{'^2}} }}} \right)' = \lambda f\left(u \right), \\ u\left(x \right) >...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020249/fulltext.html |
| Summary: | In this paper, we study the uniqueness and multiplicity of positive solutions of one-dimensional prescribed mean curvature equation \begin{equation*}\left\{ \begin{array}{l} - \left({\frac{{u'}}{{\sqrt {1 - u{'^2}} }}} \right)' = \lambda f\left(u \right), \\ u\left(x \right) > 0, - 1 < x < 1, \\ u\left({ - 1} \right) = u\left(1 \right) = 0, \end{array} \right.\end{equation*} where $\lambda$ is a positive parameter. The main tool is the fixed point index in cones. |
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| ISSN: | 2473-6988 |