Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
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DOI：
10.3934/dcdsb.2018271
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Ruyun Ma;Man Xu
中科院分区：
文献类型：
--
作者：
Ruyun Ma;Man Xu
In this paper we study global bifurcation phenomena for the Dirichlet problem associated with the prescribed mean curvature equation in Minkowski space \begin{document}$\left\{ \begin{array}{l} -\text{div}\big(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\big) = λ f(x,u,\nabla u)\ \ \ \ \ \ & \text{in}\ Ω,\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ u = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ & \text{on}\ \partial Ω.\\\end{array} \right.$\end{document} Here \begin{document} $Ω$ \end{document} is a bounded regular domain in \begin{document} $\mathbb{R}^N$ \end{document} , the function \begin{document} $f$ \end{document} satisfies the Caratheodory conditions, and \begin{document} $f$ \end{document} is either superlinear or sublinear in \begin{document} $u$ \end{document} at \begin{document} $0$ \end{document} . The proof of our main results are based upon bifurcation techniques.
In this paper we study global bifurcation phenomena for the Dirichlet problem associated with the prescribed mean curvature equation in Minkowski space \begin{document}$\left\{ \begin{array}{l} -\text{div}\big(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\big) = λ f(x,u,\nabla u)\ \ \ \ \ \ & \text{in}\ Ω,\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ u = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ & \text{on}\ \partial Ω.\\\end{array} \right.$\end{document} Here \begin{document} $Ω$ \end{document} is a bounded regular domain in \begin{document} $\mathbb{R}^N$ \end{document} , the function \begin{document} $f$ \end{document} satisfies the Caratheodory conditions, and \begin{document} $f$ \end{document} is either superlinear or sublinear in \begin{document} $u$ \end{document} at \begin{document} $0$ \end{document} . The proof of our main results are based upon bifurcation techniques.