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

We consider the curvature equation in the static spacetime, div (f(x)∇ u√1-f²(x)| ∇ u|²) +∇ u ∇ f(x)√1-f²(x)| ∇ u|²=λ NH Ω, where \(Ω\) is a bounded domain in \(R^N\), \(N ≥ 1\); 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