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We show that parameterized versions of splitting theorems in Morse theory canbe effectively used to generalize some famous bifurcation theorems forpotential operators. In particular, such generalizations based on the author'srecent splitting theorems [38, 39, 42, 43] and that of [8] are given thoughpotential operators in [42, 43] have weaker differentiability, evendiscontinuous. As applications, we obtain many bifurcation results forquasi-linear elliptic Euler equations and systems of higher order.

Parameterized splitting theorems and bifurcations for potential operators