## 留言板

 引用本文: 马世旺, 王志成, 庾建设. 在共振点的一阶微分系统的周期解[J]. 应用数学和力学, 2000, 21(11): 1156-1164.
MA Shi-wang, WANG Zhi-cheng, YU Jian-she. The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1156-1164.
 Citation: MA Shi-wang, WANG Zhi-cheng, YU Jian-she. The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1156-1164.

• 中图分类号: O175

## The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance

• 摘要: 考虑具偏差变元的一阶非线性微分系统:x>(t)=Bx(t)+F(x(t-τ))+p(t),其中,x(t)∈R2,τ∈R,B∈R2×2,F是有界的,p(t)是连续的2π-周期函数.应用Brouwer度及Mawhin重合度理论,在共振的情况下,给出了上述方程存在2π-周期解的充分条件及其在Duffing方程上的应用.
•  [1] Hale J K.Ordinary Differential Equations[M].New York:Wiley Interscience,1969. [2] Nagle R K.Nonlinear boundary value problems for ordinary differential equations with a small parameter[J].SIAM J Math Analysis,1978,9(3):719-729. [3] Mawhin J.Landesman-Lazter.stype problems for nonlinear equations[A].In:Conferenze Seminario Matematica[M].DiBari:Dell Universita,1977,147. [4] Fucik S.Solva bility of Nonlinear Equations and Boundary Value Problems[M].Dordrecht,Holland:D.Reidel Publishing,1980. [5] Nagle R K,Sinkala Z.Existence of 2π-periodic solutions for nonlinear systems of first-order ordinary differential equations at resonance[J].Nonlinear Analysis(TMA),1995,25(1):1-16. [6] MA Shi-wang,WANG Zhi-cheng,YU Jian-she.Coincidence degree and periodic solutions of Duffing equations[J].Nonlin ear Analysis(TMA),1998,34(2):443-460. [7] Lazer A C,Leach D E.Bounded perturbations of forced harmonic oscillations at resonance[J],Ann Mat Pura Appl,1969,82(1):49-68. [8] Schuur J D.Perturbation at resonance for a fourth order ordinary differential equation[J].J Math Anal Appl,1978,65(1):20-25. [9] 丁同仁.共振点的非线性振动[J].中国科学(A辑),1982,(1):1-13. [10] HAO Dun-yuan,MA Shi-wang.Semilinear Duffing equations crossing resonance points[J].J Differential Equations,1997,133(1):98-116. [11] Mawhin J.Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mapping in locally convex topological vector spaces[J].J Differential Equations,1972,12(2):610-636. [12] Mawhin J.Topolo gical Degree Methods in Nonlinear Boundary Value Problems CBMS[M].Providence RI:Amer Math Soc,1979,40. [13] Deimling K.N onlinear Functional Analysis[M].New York:Springer-Verlag,1985.

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##### 出版历程
• 收稿日期:  1998-03-25
• 修回日期:  2000-04-12
• 刊出日期:  2000-11-15

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