  We show that any general semilinear elliptic problem with Dirichlet or
Neumann boundary conditions in an annulus A in R^2m ;m >1, invariant by the
action of a certain symmetry group can be reduced to a nonhomogenous similar
problem in an annulus D in R^(m+1), invariant by another related symmetry. We
apply this result to prove the existence of positive and sign changing
solutions of a singularly perturbed elliptic problem in A which concentrate on
one or two (m-1) dimensional spheres. We also prove that the Morse indices of
these solutions tend to infinity as the parameter of concentration tends to
infinity.
