Logistic型方程周期解和概周期解的存在性

In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.     

Existence of Time Periodic Solutions to Boundary Value Problem of One-dimensional Semilinear Viscoelastic Dynamic Equation with Memory

In this paper, we prove the existence of time-periodic solutions to the boundary value problem of semilinear one-dimensional dynamical equation for viscodastic materials.     

Some Nonclassical Boundary Value Problems for Linear Mixed-Type Equations

Well-posedness of nonlocal boundary value problems is studied for some class of mixed-type equations which includes the Chaplygin equation and parabolic equations with varying time direction.     

一类非线性演化方程新的显式行波解

借助Mathematica软件和吴方法,采用双曲函数法,获得了一类非线性演化方程u_tt+au_xx+bu+cu2+du3=0的多组行波解,其中包括周期解与孤子解.这种方法也适用于其他非线性方程或方程组.     

一类高维时滞微分方程的周期解

本文考虑高维时滞微分方程ｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－ｒ（ｔ）））其中（ｔ,ｘ）∈Ｒ^ｎ,Ａ（ｔ,ｘ）是ｎ×ｎ连续矩阵,ｆ（ｔ,ｘ）是ｎ维连续向量,ｒ（ｔ）是时间依赖的滞量,应用不动点定理,在确定的条件下,证明了该系统的周期解的存在性与唯一性     

人口动力学中一类含时滞周期反应—扩散方程的正周期解分歧

本文研究人口动力学中一类含时滞周期反应-扩散方程的正周期解问题;利用紧算子的全局分歧结果给出了这个方程正周期解存在的充分必要条件。     

一类里卡提方程的两个周期解的存在性和稳定性

研究了一类里卡提方程,得到了方程的两个周期解的存在性和稳定性的充分性条件.     

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities,

where and are positive constants and is a positive -periodic function. We obtain sharp bounds for such that has exactly three ordered -periodic solutions. Moreover, when is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.

     

ALMOST PERIODIC SOLUTIONS OF NONLINEAR DUFFING'S EQUATIONS WITH DELAY

1Introduction:Recellt,lyIt.SchlniltandJa,nJ(lsit.Ward,JR.[l]developedamclfllo(1forestablishillgtheexistellceofalmostperiodicsolutionstonolllillcal'secorl'1order相似文献   

布鲁塞尔振子系统的Hopf分歧及周期振动解

利用Hopf分歧理论证明了布鲁塞尔振子系统在平衡点小振幅周期振动解的存在性.     

Positive periodic solutions for a class of delay differential equations

In this paper, we employ fixed point theorem and functional equation theory to study the existence of positive periodic solutions of the delay differential equation

x^′(t)=α(t)x(t)-β(t)x²(t)+γ(t)x(t-τ(t))x(t).     

Lyapunov exponents of solutions to linear differential equations with periodic forcing functions

We give Lyapunov exponents of solutions to linear differential equations of the form x^′=Ax+f(t), where A is a complex matrix and f(t) is a τ-periodic continuous function. Notice that f(t) is not “small” as t→∞. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear differential equations with periodic forcing functions, J. Difference Equ. Appl. 11 (2005) 1-19] of solutions to the above equation.     

一类二阶微分方程周期解的存在性

研究二阶非线性滞后型微分方程x。(t)+P[x(。t)]+Q[x(。t)]R[x(t-r)]=f(t)通过Lyaponov方法给出了ω-周期解的存在性定理和时滞范围的简明表达式,推广了一些原有结果.     

二阶常系数中立型方程的周期解

讨论了一类二阶常系数中立型方程的周期解的存在性与唯一性，获得了保证周期解存在唯一的具体条件。     

ON A PERIODIC DELAY LOGISTIC TYPE POPULATION MODEL

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｏｗｉｎｇｐｅｒｉｏｄｉｃｄｅｌａｙＬｏｇｉｓｔｉｃｔｙｐｅｐｏｐｕｌａｔｉｏｎｄＮ（ｔ）ｄｔ＝ｒ（ｔ）Ｎ（ｔ）１－ｘ（ｔ－τ（ｔ）Ｋ（ｔ）θ，（１．１）ｗｉｔｈａｎｉｎｉｔｉａｌｃｏｎｄｉｔｉｏ...     

Periodic problem for a nonlinear‐damped wave equation on the boundary

In this work we investigate the existence of periodic solutions in t for the following problem: We employ elliptic regularization and monotone method. We consider $\mbox{\boldmath{$\Omega$}}\mbox{\boldmath{$\subset$}}{\mathbb{R}}^{{{n}}} \ (n\geqslant 1)$ an open bounded set that has regular boundary Γ and Q=Ω ×(0,T), T>0, a cylinder of ${\mathbb{R}}^{n+1}$ with lateral boundary Σ = Γ × (0,T). Copyright © 2009 John Wiley & Sons, Ltd.     

SUBNORMAL SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

In this article, we apply the concept of hyper-order to higher order linear differential equations with periodic coefficients, investigate the existence and the form of its subnormal solution, and estimate the growth of all other solutions, and answer the question raised by Gundersen and Steinbart for more general periodic differential equations.     

PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

1 IntroductionThe problem of periodic solutions of nonlineax dtherential equations has been one Of thecenter problem to the tI1eory of differelltial equatiol1, it 11as wide application baCkground(8uchas fOrce oscillatioll of telecomnmnication, periodic euvironment in econondc system, etc.), soit has been a popular subject in the research work. In this paperl we discuss the problem ofperiodic solutions of the fOllowing nolllinear lleutral functional differential equatiollsd,dtD(ft xt) = f(f, …