一类非线性中立型微分方程周期解的存在性.pdfVIP

第27卷第4期 数学理论与应用 Voi．27 No．4 2007年l2月 MATHEMATlCAL THEORY AND APPLlCATlONS Dec．2007 Existence of periodic sol utions for a kind of nonlinear neutral differential equation Ou Xiaobo I iu Xinge (School of Math．Science and Computing Technology，Central South University，Changsha，410083) Abstract Using inequality techniques，a priori estimate for a periodic solution to a kind of nonlinear neutral differential equations is obtained．Basing on this priori estimate and coincidence degree theory，new result is provided concerning the existence of 2 7v——periodic solutions for a kind of neutral differential equation with delay． Keywords Neutral differential equation Dely Periodic solution Existenc 一 类非线性中立型微分方程周期解的存在性 欧小波 刘心歌 (中南大学数学科学与计算技术学院，长沙，410083) 摘 要 利用有关不等式，本文首先获得一类非线性中立型微分方程 一个新的先验估计．基于解的先验估计 以及迭合度理论，给出了这类中立型微分方程存在周期解的一个充分条件 关键词 中立型微分方程 时滞 周期解 存在性 迭合度 1 Introduction Peroodic solutions to several types of second order differential equations with delays were studied(see，for example’[1]一[2])．Recently，I u et a1．[3]discussed a kind of neutral differential equation with a deviating argument in the following form (．r(f)+f．z(f一， )) + ( (f))+g(z(f—r(f))一P(￡) (1) where C ∈R are two constants，f，g，p and r are real continuous functions defined on R．r and P are periodic with period 27『．Tile main purpose of this paper is to establish a new sufficient condition for the existence of 27『一periodic solutions of Eq．(1) 2 Main lemmas 1．et C2 一{．r 1．r∈C(R，R)， (f+27r)一 z(t)}with the norm l l。一max 9(t)l，V ∈C2 t∈[0．2 ] 蔡海涛教授推荐 收稿}