By the iteration of the KAM, the following second- order differential equation （ Фp （x′））′ ＋ F（x, x′, t） ＋ ω^PФp （x′） ＋α│x│^l ＋e（x, t） =0 is studied, where Фp（S） = │S│^p-2s, p 〉 1, α〉 0...By the iteration of the KAM, the following second- order differential equation （ Фp （x′））′ ＋ F（x, x′, t） ＋ ω^PФp （x′） ＋α│x│^l ＋e（x, t） =0 is studied, where Фp（S） = │S│^p-2s, p 〉 1, α〉 0 and ω 〉 0 are positive constants, and l satisfies - 1 〈ω 〈p ＋ 2. Under some assumptions on the parities of F（x, x′, t） and e （x, t）, by a small twist theorem of reversible mapping, the existence of quasi-periodic solutions and boundedness of all the solutions are obtained.展开更多
基金The National Natural Science Foundation of China(No. 11071038)the Natural Science Foundation of Jiangsu Province(No. BK2010420)
文摘By the iteration of the KAM, the following second- order differential equation （ Фp （x′））′ ＋ F（x, x′, t） ＋ ω^PФp （x′） ＋α│x│^l ＋e（x, t） =0 is studied, where Фp（S） = │S│^p-2s, p 〉 1, α〉 0 and ω 〉 0 are positive constants, and l satisfies - 1 〈ω 〈p ＋ 2. Under some assumptions on the parities of F（x, x′, t） and e （x, t）, by a small twist theorem of reversible mapping, the existence of quasi-periodic solutions and boundedness of all the solutions are obtained.
