  In this paper, we study positive one-dimensional solutions (i.e., solutions
that depend only on one variable) for a class of semilinear elliptic problems
in bounded cylinders in $\mathbb R^N$, $N \geq 2$. We compute the Morse index
of such solutions and deduce from it the existence of least-energy solutions
which are not one-dimensional, under suitable hypotheses on the nonlinearity
and on the base of the cylinder. Furthermore, we analyze the appearance of more
positive solutions, bifurcating from the one-dimensional ones, when we scale
the base.
