Boundedness of Solutions for a Class of Semilinear Oscillators

IF 0.8 3区 数学 Q2 MATHEMATICS
Yan Zhuang, Daxiong Piao, Yanmin Niu
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引用次数: 0

Abstract

We are concerned with the boundedness for the equation x″ + f(x, x′) + ω2x = p(t), where p is quasi-periodic function. Since the corresponding system is non-Hamiltonian, we transform the original system into a new reversible one, the Poincaré mapping of which satisfies the twist theorem for quasi-periodic reversible mappings of low smoothness, or is close to its linear part by normal form theorem. We then obtain results concerning the boundedness of solutions based on the recently work. The above two cases need some smooth and growth assumptions for f and p, which are precisely the innovations of this paper.

一类半线性振子解的有界性
研究方程x″+ f(x, x ') + ω2x = p(t)的有界性,其中p为拟周期函数。由于对应的系统是非哈密顿系统,我们将原系统变换为一个新的可逆系统,其庞卡罗映射满足低平滑准周期可逆映射的扭转定理,或者通过正规形式定理接近其线性部分。在此基础上,我们得到了关于解的有界性的一些结果。上述两种情况都需要对f和p做一些平滑和增长假设,这正是本文的创新之处。
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
138
审稿时长
14.5 months
期刊介绍: Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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