非线性中立型微分方程非振动解的渐近性

本文得到一类非线性中立型微分方程非振动解的渐近性     

Bounded Solutions of Some Second Order Nonlinear Differential Equations

We prove Landesman–Lazer type existence conditions forthe solutions bounded on the real line, together with theirfirst derivatives, for some second order nonlinear differentialequations of the form x'+cx'+f(t, x)=0. The proofs use upperand lower solutions techniques together with some limiting arguments.     

On Bounded Solutions of Systems of Linear Functional Differential Equations

Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established.     

On Periodic Solutions of Nonlinear Functional Differential Equations

Sufficient conditions are established for the existence and uniqueness of an -periodic solution of the functional differential equation where f is a continuous operator acting from the space of n-dimensional -periodic continuous vector functions into the space of n-dimensional -periodic and summable on [0,] vector functions.     

一阶非线性中立型方程组的非振动解的存在性

利用Krasnoselskii不动点定理,得到了一阶非线性中立型方程组[x_i(t) sum from j=1 to n c_(ij)x_j(t-σ)]′ f_i(t,x_l(g_(il)(t)),…,x_n(g_(in)(t)))=0,i=1,2,…,n存在趋于具均为正(负)分量的常向量的非振动解的充分必要条件.     

分数阶微分方程非振动解的存在性

考虑带强迫项分数阶中立型微分方程,利用Krasnoselskii's不动点定理获得了其一个新的非振动解存在的充分条件.     

非线性中立型差分方程正确的存在性

利用压缩映射原理，讨论了非线性中立型差分方程正解的存在性．     

具有分布时滞的高阶非线性中立型微分方程非振动解的存在性

考虑一类具有分布时滞的高阶非线性中立型微分方程,利用Banach压缩映像原理得到了非振动解存在的新的充分条件.     

二阶非线性泛函微分方程的周期解

利用Mawhin的重合度理论,研究了二阶非线性泛函微分方程周期解的存在性.     

一阶非线性泛函微分方程的周期解

本文研究了一阶非线性泛函微分方程的周期解,得到了周期解存在唯一的一些充分条件,推广和改进了这方面的已有结果。     

高阶泛函方程解的非振动准则

研究一类高阶非线性泛函微分方程用x(g(t)=p(x)x(t)+Q(t)multiply from i=1to m|x(gki+1(t))|aisgnx(gki+1(t))迭代方法获得方程解的一些新的非振动准则.并且给出了在差分方程中的应用.     

Nonoscillatory Solutions of Delay and Neutral Singular Differential Equations

A new nonoscillatory theory is presented for delay and neutral differential equations. In particular our nonlinearity may be singular in both the dependent and independent variables.     

有界时滞非线性随机微分方程解的振动性和非振性

研究了一类非线性随机时滞微分方程解的振动性和非振性,其中设定时滞可变且有界.依据该方程漂移项和扩散项的性质,证明了通过选定适当的初值,方程依概率存在正解;同时,给出了方程解几乎必然振动的一个充分条件.     

偶数阶非线性微分方程有界正解的存在性

考虑偶数阶非线性中立型微分方程,利用Lebesgue控制收敛定理获得了最终有界正解存在的一个充分必要条件.     

一类非线性泛函微分方程的周期解

研究了一类非线性滞后型泛函微分方程周期解的存在性问题.通过Ляпунов方法给出了存在周期解的充分条件和时滞范围的简明表达式,并推广了若干已知结果.     

On the Asymptotic Behavior of Nonoscillatory Solutions of Certain Fractional Differential Equations

We present the conditions under which every nonoscillator solution x(t) of the forced fractional differential equation

$$\begin{aligned} ^{\mathrm{C}}D_{\mathrm{c}}^{\alpha } y ( t ) = e ( t ) +f ( {t, x ( t )} ), c > 1,\alpha \in ( {0,1} ), \quad \mathrm{{and}} \,\, \delta \ge 1, \end{aligned}$$

where \(y(t)= ( {a(t) ( {{x}'(t)} )^{\delta }})^{\prime },c_0 =\frac{y(c)}{\Gamma (1)}= y(c)\), is a real constant which satisfies

$$\begin{aligned} |x(t)|=O\left( {t^{1/\delta }e^{t}\int _{\mathrm{c}}^{t} {a^{-1/\delta }} (s)\mathrm{d}s} \right) , \quad t \rightarrow \infty \end{aligned}$$

It is shown that the technique can be applied to some related fractional differential equations. Examples are inserted to illustrate the relevance of the obtained results.

     

Periodic Solutions for Nonlinear Diferential Equations

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非线性向量泛函微分方程解的振动比较定理

本文借助交换与不等式等方法将非线性向量泛函微分方程解的振动性与相应数量微分不等式是否存在正解作比较,得到若干振动比较定理并给出了具体应用.