  We show that parameterized versions of splitting theorems in Morse theory can
be effectively used to generalize some famous bifurcation theorems for
potential operators. In particular, such generalizations based on the author's
recent splitting theorems [38, 39, 42, 43] and that of [8] are given though
potential operators in [42, 43] have weaker differentiability, even
discontinuous. As applications, we obtain many bifurcation results for
quasi-linear elliptic Euler equations and systems of higher order.
