Boundedness of Solutions for Duffing Equation with Low Regularity in Time

It is shown that all solutions are bounded for Duffing equation x+ x^(2n+1)+2∑i=nPj(t)x^j= 0, provided that for each n + 1 ≤ j ≤ 2 n, P_j ∈ C^y(T^1) with γ > 1-1/n and for each j with 0 ≤ j ≤ n, Pj ∈ L(T^1) where T^1= R/Z.

It is shown that all solutions are bounded for Duffing equation s＋ x^2n＋1＋j=0∑^2n Pj（t）x^j=0,provided that for each n ＋ 1≤j≤2n,Pj ∈ C^γ（T^1） with γ〉1-1/n and for each j with 0 ≤ j ≤ n,Pj ∈L （T^1） where T^1=R/Z.