Abstract
In this paper, we prove the boundedness of all solutions for the periodic equation x ″ + ω 2 x + ϕ ( x ) = G x ( x , t ) + p ( t ) , where ω satisfies the Diophantine condition, ϕ ( x ) ∈ C 19 is bounded, p ( t ) ∈ C 23 and D x i D t j G ( x , t ) is bounded for 0 ⩽ i + j ⩽ 21 .
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