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
We study the global existence of solution to one di- mensional convection-diffusion equation. Through constructing a Cauchy sequence in a Banach space, we get the local existence of solution to the equation, t3ased on...We study the global existence of solution to one di- mensional convection-diffusion equation. Through constructing a Cauchy sequence in a Banach space, we get the local existence of solution to the equation, t3ased on the global bounds of the solu- tion, we extend the local one to a global one that decays in Hl space.展开更多
We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficien...We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.展开更多
Let M be a compact Riemann surface, h（x） a positive smooth function on M, and Ф（x） a smooth function on M which satisfies that ∫MeФdVg = 1. In this paper, we consider the functionalJ（u）=1/2∫M｜△u｜2eФdVg＋...Let M be a compact Riemann surface, h（x） a positive smooth function on M, and Ф（x） a smooth function on M which satisfies that ∫MeФdVg = 1. In this paper, we consider the functionalJ（u）=1/2∫M｜△u｜2eФdVg＋8πc∫MueФ-8πclog∫Mheu＋ФdVg.We give a sufficient condition under which J achieves its minimum for c ≤ infx∈MeФ（X）.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.
基金Supported by the National Natural Science Foundation of China(11101121)
文摘We study the global existence of solution to one di- mensional convection-diffusion equation. Through constructing a Cauchy sequence in a Banach space, we get the local existence of solution to the equation, t3ased on the global bounds of the solu- tion, we extend the local one to a global one that decays in Hl space.
文摘We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.
文摘Let M be a compact Riemann surface, h（x） a positive smooth function on M, and Ф（x） a smooth function on M which satisfies that ∫MeФdVg = 1. In this paper, we consider the functionalJ（u）=1/2∫M｜△u｜2eФdVg＋8πc∫MueФ-8πclog∫Mheu＋ФdVg.We give a sufficient condition under which J achieves its minimum for c ≤ infx∈MeФ（X）.
