The existence of harmonic maps from an annulus toS 2 with symmetric boundary value

In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere inℝ ³ with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary value isS ¹-equivariant and nonconstant. This research partially supported by the NNSF, P.R. China.