Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 48, pp. 1-10.

Title: Local bifurcation structure and stability of the mean curvature equation in the static spacetime

Authors: Siyu Gao  (Dalian Univ. of Tech., Dalian, China)
         Qingbo Liu (Dalian Univ. of Tech., Dalian, China)
         Yingxin Sun (Dalian Univ. of Tech., Dalian, China)

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.