We extend two stability theorems due to Howard and Okayasu to the case of $F$-harmonic maps. In fact we show that every stable $F$-harmonic map into sufficiently pinched simply-connected Riemannian manifold is constant.
"Stability of $F$-harmonic maps into pinched manifolds." Hiroshima Math. J. 31 (1) 171 - 181, March 2001. https://doi.org/10.32917/hmj/1151511154