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

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.    For more information see https://ejde.math.txstate.edu/Volumes/2024/48/abstr.html