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\title{The Gelfand Problem in Tubular Domains}

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\abstract{We construct stable solutions of $\Delta u + \lambda e^u=0$ with
Dirichlet boundary conditions in small tubular domains (i.e.\ geodesic
$\ep$--neighbourhoods of a curve $\Lambda$ embedded in $\RR^n$), 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, $\Lambda$ can be replaced by any compact smooth
manifold embedded in $\RR^n$.}
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\input{sections/introduction}
\input{sections/preliminaries}
\input{sections/stable-solutions-in-the-tube}
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% \input{sections/unstable-less-than-11}
\input{sections/concluding-remarks}
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