摘要
为了拓展Duffing方程周期解的存在性和渐近稳定性的研究方法,在较弱的周期和反周期特征值条件下,基于Lyapunov稳定性理论和LeraySchauder型存在性定理,验证Duffing方程的周期解的存在性、唯一性和渐近稳定性.结果表明,当λ∈[0,1]和||x||≥R时,Duffing方程有x∈domL,H(x,λ)≠0,且唯一的周期为T的解x_(0)的衰变率是c/2,与X的初始值无关.
In order to expand the research methods for the existence and asymptotic stability of periodic so-lutions of the Duffing equation,based on the Lyapunov stability theory and Leray Schauder type existence theo-rem under weak periodic and anti periodic eigenvalue conditions,the existence,uniqueness and asymptotic sta-bility of periodic solutions of the Duffing equation are verified.The results indicate that,when λ∈[0,1]and||x||≥R,the Duffing equation has x ∈ dom L,H(x,λ)≠0,and the decay rate of the unique solution x_(0) with a period of T is 2,independent of the initial value of X.
作者
王从徐
WANG Congxu(Chuzhou City Vocation College,Chuzhou 239000,Anhui,China)
出处
《山西师范大学学报(自然科学版)》
2025年第3期1-4,共4页
Journal of Shanxi Normal University(Natural Science Edition)
基金
安徽省高等学校人文社会科学重点研究项目(SK2021A0978)。
