## 留言板

 引用本文: 葛渭高. 周期外力作用下某些二阶非线性微分方程的调和解[J]. 应用数学和力学, 1985, 6(10): 929-937.
Ge Wei-gao. Harmonic Solutions of Some Second-Order Nonlinear Equations under a Periodic Force[J]. Applied Mathematics and Mechanics, 1985, 6(10): 929-937.
 Citation: Ge Wei-gao. Harmonic Solutions of Some Second-Order Nonlinear Equations under a Periodic Force[J]. Applied Mathematics and Mechanics, 1985, 6(10): 929-937.

## Harmonic Solutions of Some Second-Order Nonlinear Equations under a Periodic Force

• 摘要: 本文给出了某些二阶非线性微分方程在周期外力作用下存在调和解的若干定理.这些定理推广了文[1]～[8]的有关结果.
•  [1] Lefschitz.S.,Existence of periodic solutions for certain differential equations,Proc.Nat.,Ac.Sci.,29(1943),29-32. [2] Levinson,N.,On the existence of periodic solutions for second order differential equations with a forcing term,Jour.Math.Phys.,22(1943). [3] De Castro.A.,Sulle oscillazioni non lineari dei sistemi di uno o piúgradi diliberta,Rend.Sem.Mat.Univ.,22(1953). [4] Reuter,G.E.H.,A boundedness theorem for nonlinear differential equations of second order,Proc.Cambr.Phil.Soc.,47(1951). [5] Mizohata,S.and M.Yamaguti,On the existence of periodic solutions of the non-linear differential equation x+a(x)x+φ(x)=p(t),Mem.Coll.Sci.Kyoto Univ.,Ser.A,27(1952). [6] Graef,J.R.,On the generalized liénard equation with negative damping,J.Diff.Eqs.,12(1972). [7] 李曾淑、王墓秋,论具有阻尼的Duffing方程的周期解,科学通报,22(1980) [8] Ascari.A.,Studio asintotico di unequatione relativa alla dinamica del punto.Rend.Ist Lamb.Sci.Lett.,16,2(1952). [9] 秦元勋、王联、王慕秋,《运动稳定性理论与应用》,科学出版社(1981). [10] 贺建勋,关于不连续系统的普遍唯一性定理,数学学报,26,3(1983).

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##### 出版历程
• 收稿日期:  1984-07-31
• 刊出日期:  1985-10-15

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