On a power-type coupled system with mean curvature operator in Minkowski space
Abstract We study the Dirichlet problem for the prescribed mean curvature equation in Minkowski space { M ( u ) + v α = 0 in B , M ( v ) + u β = 0 in B , u | ∂ B = v | ∂ B = 0 , $$ \textstyle\begin{cases} \mathcal{M}(u)+ v^{\alpha }=0\quad \text{in } B, \\ \mathcal{M}(v)+ u^{\beta }=0\quad \text{i...
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2021
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oai:doaj.org-article:98a5f53631bd4b9e8eaa9e8004cb510e2021-11-21T12:07:16ZOn a power-type coupled system with mean curvature operator in Minkowski space10.1186/s13661-021-01572-z1687-2770https://doaj.org/article/98a5f53631bd4b9e8eaa9e8004cb510e2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13661-021-01572-zhttps://doaj.org/toc/1687-2770Abstract We study the Dirichlet problem for the prescribed mean curvature equation in Minkowski space { M ( u ) + v α = 0 in B , M ( v ) + u β = 0 in B , u | ∂ B = v | ∂ B = 0 , $$ \textstyle\begin{cases} \mathcal{M}(u)+ v^{\alpha }=0\quad \text{in } B, \\ \mathcal{M}(v)+ u^{\beta }=0\quad \text{in } B, \\ u|_{\partial B}=v|_{\partial B}=0, \end{cases} $$ where M ( w ) = div ( ∇ w 1 − | ∇ w | 2 ) $\mathcal{M}(w)=\operatorname{div} ( \frac{\nabla w}{\sqrt{1-|\nabla w|^{2}}} )$ and B is a unit ball in R N ( N ≥ 2 ) $\mathbb{R}^{N} (N\geq 2)$ . We use the index theory of fixed points for completely continuous operators to obtain the existence, nonexistence and uniqueness results of positive radial solutions under some corresponding assumptions on α, β.Zhiqian HeYanzhong ZhaoLiangying MiaoSpringerOpenarticleMinkowski curvature operatorSystemPositive radial solutionUniquenessAnalysisQA299.6-433ENBoundary Value Problems, Vol 2021, Iss 1, Pp 1-9 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
Minkowski curvature operator System Positive radial solution Uniqueness Analysis QA299.6-433 |
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Minkowski curvature operator System Positive radial solution Uniqueness Analysis QA299.6-433 Zhiqian He Yanzhong Zhao Liangying Miao On a power-type coupled system with mean curvature operator in Minkowski space |
| description |
Abstract We study the Dirichlet problem for the prescribed mean curvature equation in Minkowski space { M ( u ) + v α = 0 in B , M ( v ) + u β = 0 in B , u | ∂ B = v | ∂ B = 0 , $$ \textstyle\begin{cases} \mathcal{M}(u)+ v^{\alpha }=0\quad \text{in } B, \\ \mathcal{M}(v)+ u^{\beta }=0\quad \text{in } B, \\ u|_{\partial B}=v|_{\partial B}=0, \end{cases} $$ where M ( w ) = div ( ∇ w 1 − | ∇ w | 2 ) $\mathcal{M}(w)=\operatorname{div} ( \frac{\nabla w}{\sqrt{1-|\nabla w|^{2}}} )$ and B is a unit ball in R N ( N ≥ 2 ) $\mathbb{R}^{N} (N\geq 2)$ . We use the index theory of fixed points for completely continuous operators to obtain the existence, nonexistence and uniqueness results of positive radial solutions under some corresponding assumptions on α, β. |
| format |
article |
| author |
Zhiqian He Yanzhong Zhao Liangying Miao |
| author_facet |
Zhiqian He Yanzhong Zhao Liangying Miao |
| author_sort |
Zhiqian He |
| title |
On a power-type coupled system with mean curvature operator in Minkowski space |
| title_short |
On a power-type coupled system with mean curvature operator in Minkowski space |
| title_full |
On a power-type coupled system with mean curvature operator in Minkowski space |
| title_fullStr |
On a power-type coupled system with mean curvature operator in Minkowski space |
| title_full_unstemmed |
On a power-type coupled system with mean curvature operator in Minkowski space |
| title_sort |
on a power-type coupled system with mean curvature operator in minkowski space |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/98a5f53631bd4b9e8eaa9e8004cb510e |
| work_keys_str_mv |
AT zhiqianhe onapowertypecoupledsystemwithmeancurvatureoperatorinminkowskispace AT yanzhongzhao onapowertypecoupledsystemwithmeancurvatureoperatorinminkowskispace AT liangyingmiao onapowertypecoupledsystemwithmeancurvatureoperatorinminkowskispace |
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1718419201218052096 |