方程a2(x)(t-τ)+a1(x)(t-τ)+a0x(t-τ)+b2(x)(t)+b1(x)(t)+b0x(t)=δ的部分解讨论

讨论了方程a2(x)(t-τ)+a1(x)(t-τ)+a0x(t-τ)+b2(x)(t)+b1(x)(t)+b0x(t)=δ的部分解.     

一类二阶中立型微分差分方程周期解的存在性

考虑如下二阶中立型微分差分方程的边值问题：{x(t-τ)-x(t-τ） f(t,x(t),x(t-τ）,x(t-2τ）=0 x(0)=x(2kτ），x（0）=x（2kτ）其中k是任意给定的正整数,τ 为正实数，利用含有偏差变元的变分结构及临界点理论，作给出了判定上述方程存在非平凡周期解的判定准则。     

一类二阶混合型泛函微分方程多重周期解

本文利用变分原理和Z2不变群指标研究了二阶混合型泛函微分方程x"(t-τ) f(t,x(t),x(t-τ),x(t-2τ))=0和x"(t-r) λf1(t,x(t),x(t-τ),x(t-2τ))=x(t-τ)多重周期解．得出了有关新结果．     

变参数的高阶中立型微分方程周期解的存在性

利用Mawhin重合度理论,本文研究如下变参数的高阶中立型泛函微分方程[x(t)+c(t)x(t-τ)](n)+f1(x(t))x′(t)+f2(x′(t))x″(t)+g(t,x(t-σ))=p(t)周期解的存在性,给出这类高阶微分方程至少存在一个T周期解的充分性条件.     

一类三阶具偏差变元微分方程的周期解

利用重合度理论研究一类三阶具偏差变元微分方程x(t)+ax″(t)+bx′(t)+cx(t)+g(x(t-τ(t)))=p(t)的2π-周期解问题,得到了存在2π-周期解的充分条件.     

具有正负系数的连续变量的差分方程解的零点分布

考虑具有正负系数的连续变量的差分方程 x(t)-x(t-γ)+P(t)x(t-τ)-Q(t)x(t-σ)=0,其中P,Q∈C([t_0,∞),R~+),τ,σ,γ∈(0,∞)。本文给出了上述方程解的零点分布及方程所有解振动的充分条件并改进和推广了已有的结果。     

Variational Iteration Method for Delay Differential Equations

Since1930'sand40's,theexamplesofdelaydifferentialequationsarisinginpracticalapplicationshavebeenescalatedrapidly,andhavebeenstudiedextensively(fordetails,see[1]).Inthispaperwewillproposeanovelmethodcalledvariationaliterationmethod[2]tosolvesuchproblems.Considerfollowingpopulationgrowthmodel[1]x′(t)+cθ(t-1)x(t)+cθ(t-1)=0(1a)x(0)=θ(0),-1≤t≤0(1b)　　Accordingtovariationaliterationmethod[2],thecorrectionfunctionalcanbeconstructedasfollowsxn+1(t)=xn(t)+∫t0λ[x′nτ+cθ(τ-1)xn(τ)+cθ(τ-1…     

一类二阶中立型泛函微分方程的无穷多个次调和周期解

本文通过变分原理和Z2不变群指标,得出了下述二阶中立型泛函微分方程存在无穷多个次调和周期解的充分条件(p(t)(μx′(t)) x′(t-τ) μx′(t-2τ))′-q(t)x(t) f(t,x(t),x(t-τ),x(t-2τ))=0,|μ|＜1/2.     

分数阶微分方程非振动解的存在性

考虑分数阶具有正负系数中立型微分方程Dtα[r(t)x(t)+P (t)x(t-θ)]-q1(t)g1(x(t-τ))+q2(t)g2(x(t-σ))=h(t),利用Banach压缩映像原理获得了其一个新的非振动解的存在的充分条件.     

具有偏差变元的Li\''{e}nard型方程的周期解

本文利用重合度理论研究了一类具偏差变元的Li\'{e}nard型方程$x'(t)+f_1(t,x(t))|x'(t)|^2+f_2(t,x(t),x(t-\tau_{0}(t)))x'(t)+g(t,x(t-\tau_{1} (t)))=p(t).$获得了该方程存在$\omega$-周期解的若干新结论, 改进和推广了已有文献中的相关结果.     

关于一个二阶非线性中立时滞微分方程的非振荡解的存在性

A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.     

ASYMPTOTIC STABILITY FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

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具连续变量的高阶中立型时滞差分方程的振动性

In this paper, we study oscillation of solutions for a class of high order neutral delay difference equations with variable coefficients -τm [x(t) - c(t)x(t - τ)] = (-1)mp(t)x(t - σ), t ≥ t0 0. Some sufficient conditions are obtained for bounded oscillation of the solutions.     

二阶线性中立时滞方程非振动解的存在性

考虑具有正负系数的中立时滞微分方程这里P∈R和τ∈(0,∞),σ1,σ2∈[0,∞)且Q1,Q2∈C([t0,∞),R+).对于上面方程非振动解的存在性,得到一个用,∫sQids <∞,i=1,2,来表达的充分条件。这个结果去掉了M.R.S.Kulenovic和S.Hadziomerspahic文中一个相当强的假设,改进了其中的相关定理.     

带一类时滞项的生物种群扩散模型的行波解

本文利用Schauder不动点理论证明了微分积分方程组行波解u（x，t）＝U（z）,w（x,t）＝W（z）,z＝xγ－ct的存在性．这个方程组描述了一类在植物上繁殖，且靠飞行在空中扩散的生物种群扩散过程．特别当时滞项，中积分核K（t）（反映种群繁殖模式）属于L1（0，∞）时，本文得到极限值W（－∞）（表示最终植物上种群密度）小于M．这个结论较符合生物实际．     

一类具复杂偏差变元的中立型微分方程的周期解

本文研究了一类具复杂偏差变元的中立型泛函微分方程■(t)=θ■(t-r) α(t)f(x(t)) β(t)g(x(x(t))) p(t)的周期解的存在性,得到了周期解存在的充分条件,并给出了所得结论的几个简单应用．     

Periodic solutions for a type of neutral system with variable parameters

In this paper, we firstly analyze some properties of the linear difference operator $[Ax](t)=x(t)-C(t)x(t-\tau),$ where $C(t)$ is a $n\times n$ matrix function, and then using Mawhin''s continuation theorem, a first-order neutral functional differential system is studied. Some new results on the existence and stability of periodic solutions are obtained. The results are related to the deviating arguments $\tau$ and $\mu$. Meanwhile, the approaches to estimate a $prior$ bounds of periodic solutions are different from the corresponding ones of the known literature.     

An Inverse Coefficient Problem for an Integro-differential Equation

In this article we consider the inverse coefficient problem of recovering the function { ( x ) system of partial differential equations that can be reduced to a second order integro-differential equation $ -u_{xx} + c(x)u_{x} + d\phi (x)u-\gamma d\phi (x)\int _{0}^{t}e^{-\gamma (t-\tau )}u(x,\tau )\, d\tau = 0 $ with boundary conditions. We prove the existence and uniqueness of solutions to the inverse problem and develop a numerical algorithm for solving this problem. Computational results for some examples are presented.     

一类具时滞的Liénard型方程的周期解

利用重合度理论研究了一类具时滞的Liénard型 方程x'+f_1(x)|x'|^2+f_2(t,x(t),x(t-\delta(t)))x'+g(t,x(t-\tau(t)))=p(t).获得了该方程存在T-周期解的若干新结论, 改进推广了有关文献中的已有结果.