Stability and constant boundary-value problems of harmonic maps with potential

Let M, N be Riemannian manifolds, f : M --> N a harmonic map with potential H, namely, a smooth critical point of the functional E-H(f) = integral(M)[ e(f) - H(f)], where e(f) is the energy density of f. Some results concernin g the stability of these maps between spheres and any Riemannian manifold a re given. For a general class of M, this paper also gives a result on the c onstant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.