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具复杂偏差变元的二阶中立型微分方程周期解

Periodioc Solutions to a Type of Second Order Neutral Functional Differential Equaiton with Complex Deviating Argument
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摘要 利用重合度方法,研究一类具复杂偏差变元的二阶中立型泛函数分方程[x(t)-∑i=1cix(t-iτ)]″+g(x(t))+g(x(x(t)))=p(t)周期解的存在性,给出了该方程存在周期解的充分性定理. The existence of periodic solutions to a type of second order neutral functional differential equation [x（t）-∑i=1^ncix（t-τi）]^n＋g（x（t））＋g（x（x（t）））=p（t）with complex deviating argument is studied by the methods presented in coincidence degree theory. And sufficient conditions of the equation with penocllc solutions are obtained.
作者 文乾 鲁世平
机构地区 安徽师范大学数学计算机科学学院
出处 《安徽师范大学学报（自然科学版）》 CAS 2007年第2期108-111,115,共5页 Journal of Anhui Normal University(Natural Science)
基金 安徽省自然科学基金(No.050460103) 安徽省教育厅自然科学基金重点项目(2005kj0321zD)资助
关键词 中立型泛函微分方程 周期解 重合度理论 neutral functional differential equation periodic solution theory of coincidence degree
分类号 O175.14 [理学—基础数学]
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二级参考文献11

  • 1Hale, J, K, Mawhin, J.: Coincidence degree and periodic solutions of neutral equations. J. Diff. Eqns,15, 295-307 (1975).
  • 2Fan, M, Wang, K.: Periodic solutions of convex neutral functional differential equations, Tohoku J. Math,52, 47-49 (2000).
  • 3Hale, J. K.: Theory of functional differential equations, Springer-Verlag, New York, 1977.
  • 4Bartsch, Th, Mawhin, J.: The Leray Schauder degree of S^1-equivariant operator associated to autonomous neutral equations in spaces of periodic functions. J. Differential Equations, 92, 90-99 (1991).
  • 5Serra, E.: Periodic solutions for some nonlinear differential equational equations of neutral type, Nonlinear Analysis, TMA, 17, 1:139-151 (1991).
  • 6Lu, S. P, Ge, W. G.: On the existence of periodic solutions for neutral functional differential equation.Nonlinear Analysis, TMA, 54, 1285-1306 (2003).
  • 7Lu, S. P, Ge, W. G.: On the existence of periodic solutions for a kind of second order n-Dimensional neutral differential equation. Aeta Mathematica Sinica, Chinese Series, 46(3), 601-610, (2003).
  • 8Lu, S. P, Ge, W. G, Zheng, Z. X.: Periodic,solutions to neutral functional differential equation with deviating arguments. Applied Mathematics and Computation, 152(1), 17-27 (2004).
  • 9Lu, S, P, Ge, W. G.: Problems of periodic solutions for a kind of second order neutral functional differential equation. Applicable Analysis, 82(5), 393-410 (2003).
  • 10Lu, S. P, Ge, W. G, Zheng, Z. X.: Existence of periodic solutions for neutral functional differential equation.Chinese Annals of Mathematics (A), 25(5), 645-652 (2004).

共引文献7

安徽师范大学学报（自然科学版）
2007年 第2期

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