Stability of generalized P-harmonic maps

In this paper, we prove that any stable P(x)-harmonic map Psi from S-2 to N is a holomorphic or anti-holomorphic map, where N is a Kahlerian manifold with non-positive holomorphic bisectional curvature and P(x) >= 2 is a smooth function on the sphere S-2 satisfying some condition. We study the existence of stable P(x)-harmonic map from sphere S-n (n > 2) to Riemannian manifold N , and the stability of P(x)-harmonic identity. We also study the case of a product S-1(n) x ... x S-k(n).