纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2013年
3期
233-240
,共8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
研究了一个三阶泛函微分方程周期解的存在唯一性和全局吸引性：x′′′(t)+ ax′′(t)+ bx′(t)+ cx(t)+ g(t, x(t ?τ))= p(t)。这是一个常系数拟线性泛函微分方程。通过将这个方程转变为三维的拟线性微分方程(组),得到了这个方程存在唯一周期解的充分条件；通过选取适当的李雅普诺夫函数,推导了这个方程解的全局吸引性；进一步,得到了此方程周期解的全局吸引性。最后,举出了两个应用实例。
研究瞭一箇三階汎函微分方程週期解的存在唯一性和全跼吸引性：x′′′(t)+ ax′′(t)+ bx′(t)+ cx(t)+ g(t, x(t ?τ))= p(t)。這是一箇常繫數擬線性汎函微分方程。通過將這箇方程轉變為三維的擬線性微分方程(組),得到瞭這箇方程存在唯一週期解的充分條件；通過選取適噹的李雅普諾伕函數,推導瞭這箇方程解的全跼吸引性；進一步,得到瞭此方程週期解的全跼吸引性。最後,舉齣瞭兩箇應用實例。
연구료일개삼계범함미분방정주기해적존재유일성화전국흡인성：x′′′(t)+ ax′′(t)+ bx′(t)+ cx(t)+ g(t, x(t ?τ))= p(t)。저시일개상계수의선성범함미분방정。통과장저개방정전변위삼유적의선성미분방정(조),득도료저개방정존재유일주기해적충분조건；통과선취괄당적리아보낙부함수,추도료저개방정해적전국흡인성；진일보,득도료차방정주기해적전국흡인성。최후,거출료량개응용실례。
This paper considers the existence, uniqueness and global attractivity of a periodic solution for a third-order functional differential equation:x′′′(t) + ax′′(t) + bx′(t) + cx(t) + g(t, x(t ? τ)) = p(t), which is a third-order quasilinear functional differential equation with constant coeffcients. By converting this equation into a three-dimensional quasilinear one, the su?cient conditions for the existence of exactly one periodic solution of this equation are established. By constructing suitable Lyapunov functionals, the global attractivity of a solution for the above equation is established; Moreover, the global attractivity of a periodic solution is established. In the last section, two examples will be provided to illustrate the applications of the results.
