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次调和解
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  subharmonic solution
     A Kind of Period Solution and Subharmonic Solution of Nonlinear Viblation System
     一类非线性振动系统的周期解及次调和解
短句来源
     Periodic and Subharmonic Solution of a Class of Hamiltonian Systems and Nontrivail Solutions of Elliptic Boundary Value Problems
     一类Hamilton系统的次调和解与周期解和椭圆型边值问题的非平凡解的存在性
短句来源
     In this paper, for the first order Hamiltonian systemsand the second order Hamiltonian systemswith the aids of variational methods, some existence results are obtained for subharmonic solution of local coercive sublinear Hamiltonian systems (HSl) and periodic solution of nonquadratic Hamiltonian systems (HS2).
     -ü(t)+A(t)u=▽F(t,u(t)) (HS2)运用变分法分别得到了局部强制条件下的次线性的系统(HS1)的次调和解和非二次条件下系统(HS2)的周期解存在性的结果; 同时也考虑了椭圆型边值问题
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     Using the Rabinowitz′s saddle point theorem and Ambrosetti-Rabinowitz′s mountain Pass theorem and the morse index extimates of the corresponding critical points,we prove the existence of the subharmonic solution with prescribed minimal period about two classes of nonautonomus Hamiltionian systems
     利用Rabinowitz鞍点定理及Ambroseti-Rabinowitz山路引理以及它们相应的临界点的Morse指标估计证明了二类非自治Hamilton系统给定极小周期的次调和解的存在性
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  subharmonic solutions
     On the Subharmonic Solutions of the Sub-Linear Duffing Equation
     关于亚线性Duffing方程的次调和解
短句来源
     The existence of harmonic solution and infinitely many subharmonic solutions for Duffing equation x″+g(x)=p(t) are proved. In the Duffing equation, g(x) is an odd function and is satisfied with g′(x)> 0 and g(x)=a> 0.The continuous 2π-periodic function, namely p(t) satisfied: |p(t)|
     摘要:证明了Duffing方程x″+g(x)=p(t)的调和解及无穷多的次调和解的存在性,其中g′(x)是奇函数,满足g'(x)>0且limfor(x→+∞)g(x)=a>0,周期为2π的连续函数p(t)满足|p(t)|
短句来源
     In the paper, we will prove the existence of harmonic solution and infinitely many subharmonic solutions for Duffing equationx + arctan x = p(t), where continuous 2π-periodic function p(t) satisfies
     本文证明了Duffing方程x+arctan x=p(t)的调和解和无穷多的次调和解的存在 性,其中周期的2π连续函数p(t)满足|p(t)|<π/2,(?) t∈R.
短句来源
     Harmonic Solutions and Subharmonic Solutions for Some Duffing Equation
     一个Duffing方程的调和解和次调和解
短句来源
     SUBHARMONIC SOLUTIONS OF SUBLINEAR DUFFING'S SYSTEMS
     次线性Duffing系统的多重次调和解
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  “次调和解”译为未确定词的双语例句
     Secondly, we discuss the existence of periodic solutions and sub-harmonic solutions of the above class of subquadratic higher-order difference equations being under the condition of positive-definited or negative-definited matrix by using minimax method.
     然后利用最大值和最小值方法讨论了这类高阶差分方程,当函数F(t,z)在无穷远点满足次二次性增长,矩阵是正定或负定矩阵时,这类高阶差分方程周期解和次调和解的存在性,得到了一些相应的结果。
短句来源
     Subharmonics for strongly asymmetric Duffing equations
     强不对称Duffing方程的次调和解
短句来源
     Subharmonics for One Class Symmetric Duffing Equations
     一类对称Duffing方程的次调和解
短句来源
     Based on the successor map and a generalized version of the Poincare-Birkhoff twist theorem, we establish the existence of infinitely many subharmonics for a class of strongly asymmetric Duffing equations.
     利用后继映射和推广的Poincare-Birkhoff扭转定理,证明了一类强不对称Duffing方程存在无穷多个次调和解.
短句来源
     We mainly make much investigation for the existence of periodic and sub-harmonic solutions of these new models.
     我们主要对这几类模型周期解和次调和解的存在性进行了较为深入的研究,获得了它们周期解和次调和解存在的新的充分条件。
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  subharmonic solution
Subharmonic solution of a piecewise linear oscillator with tow degrees of freedom
      
A 1/3 Pure Subharmonic Solution and Transient Process for the Duffing's Equation
      
The 1/3 subharmonic solution for the Duffing's equation is investigated by using the methods of harmonic balance and numerical integration.
      
A 1/3 pure subharmonic solution and transient process for the Duffing's equation
      
The 1/3 subharmonic solution for the Duffing's equation is investigated by using the methods of harmonic balance and numerical integration.
      
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  subharmonic solutions
This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations.
      
We study the regular Hopf bifurcation and singular Hopf bifurcation from a basic equilibrium, and show the existence of the subharmonic solutions by using the averaging method and perturbed methods and bifurcation equations.
      
We provide sufficient conditions for the existence and multiplicity of subharmonic solutions for Duffing's equations with jumping nonlinearities.
      
Existence of periodic and subharmonic solutions for second-order superlinear difference equations
      
By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations.
      
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The purplose of this paper is to prove the existence of intinitcly many subharmomic solutions of sub-linear Duffing equation.

本文证明了亚线性Duffing方程存在充分高阶的次调和解

This paper is to consider subharmornic solutions for a class of nonautonomous second order systems. the main result is that, under some suitable assumptions, there exists a sequence of periodic solutions of the systems such that the minimal periods are at most finitely same each other.

本文主要研究一类二阶方程组的次调和解。在适当的前提下,得到了该方程组存在一列极小周期至多只有有限个相同的周期解。

In tnis paper,we discuss the existence of the suberharmonic solutions with prescribedminimal period for a class nonautonomous nonconvex Hamilonian systems.

用Z指标理论讨论了一类非自治、非凸Hamilton方程组多个给定最小周期次调和解的存在问题。

 
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