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) >...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020249/fulltext.html |
| _version_ | 1818097116992503808 |
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| author | Zhiqian He Liangying Miao |
| author_facet | Zhiqian He Liangying Miao |
| author_sort | Zhiqian He |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T23:15:25Z |
| format | Article |
| id | doaj.art-5b72648cdc4240dfa56602e8019d3d4d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T23:15:25Z |
| publishDate | 2020-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5b72648cdc4240dfa56602e8019d3d4d2022-12-22T01:29:51ZengAIMS PressAIMS Mathematics2473-69882020-05-015438403850Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski spaceZhiqian He0Liangying Miao11 Department of Basic Teaching and Research, Qinghai University, Xining 810016, P. R. China2 School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, P. R. ChinaIn 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.https://www.aimspress.com/article/10.3934/math.2020249/fulltext.htmlmean curvature equationpositive solutionsmultiplicityuniquenesscone |
| spellingShingle | Zhiqian He Liangying Miao Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space AIMS Mathematics mean curvature equation positive solutions multiplicity uniqueness cone |
| title | Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space |
| title_full | Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space |
| title_fullStr | Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space |
| title_full_unstemmed | Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space |
| title_short | Uniqueness and multiplicity of positive solutions for one-dimensional prescribed mean curvature equation in Minkowski space |
| title_sort | uniqueness and multiplicity of positive solutions for one dimensional prescribed mean curvature equation in minkowski space |
| topic | mean curvature equation positive solutions multiplicity uniqueness cone |
| url | https://www.aimspress.com/article/10.3934/math.2020249/fulltext.html |
| work_keys_str_mv | AT zhiqianhe uniquenessandmultiplicityofpositivesolutionsforonedimensionalprescribedmeancurvatureequationinminkowskispace AT liangyingmiao uniquenessandmultiplicityofpositivesolutionsforonedimensionalprescribedmeancurvatureequationinminkowskispace |