We prove an almost global existence result for the Klein-Gordon equation with the Kirchhoff-type nonlinearity on $ \mathbb{T}^d $ with Cauchy data of small amplitude $ \epsilon $. We show a lower bound $ \epsilon^{-2N-2} $ for the existence time with any natural number $ N $. The proof relies on the method of normal forms and induction. The structure of the nonlinearity is good enough that proceeds normal forms up to any order.
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