Siyu Gao, Qingbo Liu, Yingxin Sun
Abstract:
We consider the curvature equation in the static spacetime,
$$
\text{div}
\Big(\frac{f(x)\nabla u}{\sqrt{1-f^2(x)| \nabla u|^2}}\Big)
+\frac{\nabla u \nabla f(x)}{\sqrt{1-f^2(x)| \nabla u|^2}}=\lambda NH
\quad\text{in }\Omega,
$$
where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\), \(N \geq 1\);
the function \(H\) gives the mean curvature.
We investigate the local bifurcation structure and stability of the
solutions to this equation.
Submitted July 10, 2024. Published August 26, 2024.
Math Subject Classifications: 35B32, 35J93, 35B35.
Key Words: Bifurcation; mean curvature operator; stability.
DOI: 10.58997/ejde.2024.48
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| Siyu Gao School of Mathematical Sciences Dalian University of Technology Dalian, 116024, China email: gao15898107523@163.com |
| Qingbo Liu School of Mathematical Sciences Dalian University of Technology Dalian, 116024, China email: liuqingbo@mail.dlut.edu.cn |
| Yingxin Sun School of Mathematical Sciences Dalian University of Technology Dalian, 116024, China email: sunyingxin2023@mail.dlut.edu.cn |
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