Home of https://arxiv.org/abs/1903.01833.
We construct stable solutions of Δu+λeu=0 with Dirichlet boundary conditions in small tubular domains (i.e. geodesic ε--neighbourhoods of a curve Λ embedded in ℝn), adapting the arguments of Pacard-Pacella-Sciunzi. We also show unicity of these solutions, in particular, we show that the stable branch of the bifurcation diagram is similar to the well-known nose-shaped diagram of the standard Gelfand problem in the unit ball. In this work, Λ can be replaced by any compact smooth manifold embedded in ℝn.