延边大学学报(自然科学版)
延邊大學學報(自然科學版)
연변대학학보(자연과학판)
JOURNAL OF YANBIAN UNIVERSITY(NATURAL SCIENCE EDITION)
2013年
4期
240-243,276
,共5页
泛函微分方程%周期解%唯一性%全局吸引性
汎函微分方程%週期解%唯一性%全跼吸引性
범함미분방정%주기해%유일성%전국흡인성
functional differential equation%periodic solution%uniqueness%global attractivity
研究四阶泛函微分方程x(4)(t)+a1x(t)+a2x″(t)+a3x′(t)+a4x(t)+g(t,x(t-τ))=p(t)的周期解问题。首先将该方程转变为四维的拟线性微分方程(组),得到该方程存在唯一周期解的充分条件;然后通过选取适当的李雅普诺夫函数,推导方程任一解的全局吸引性,并进一步得到方程周期解的全局吸引性。最后,通过实例证实了本文结果的正确性。
研究四階汎函微分方程x(4)(t)+a1x(t)+a2x″(t)+a3x′(t)+a4x(t)+g(t,x(t-τ))=p(t)的週期解問題。首先將該方程轉變為四維的擬線性微分方程(組),得到該方程存在唯一週期解的充分條件;然後通過選取適噹的李雅普諾伕函數,推導方程任一解的全跼吸引性,併進一步得到方程週期解的全跼吸引性。最後,通過實例證實瞭本文結果的正確性。
연구사계범함미분방정x(4)(t)+a1x(t)+a2x″(t)+a3x′(t)+a4x(t)+g(t,x(t-τ))=p(t)적주기해문제。수선장해방정전변위사유적의선성미분방정(조),득도해방정존재유일주기해적충분조건;연후통과선취괄당적리아보낙부함수,추도방정임일해적전국흡인성,병진일보득도방정주기해적전국흡인성。최후,통과실예증실료본문결과적정학성。
We consider the periodic solution for the following fourth order functional differential equation x(4)(t)+a1x(t)+a2x″(t)+a3x′(t)+a4x(t)+g(t,x(t-τ))=p(t).Firstly we obtain the sufficient condi-tions for the existence of uniqu periodic solution of this equation by converting the equation into a four-dimensi-nal quasi-linear differential equation.Then,by selecting an appropriate Lyapunov function,the global attrac-tivity of an arbitraty solution for this equation is derived,and furthermore,the global attractivity of a periodic solution for this equation is given.Finally,an example is provided to verify the correctness of the results in this paper.