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§ 1 . Introduction Recently,Li啨nard typeequationhasbeenwidelyinvestigated ,manyexcellentresultshavebeenobtained .In [1],theauthorhasinvestigatedLi啨nard typeequation¨x +f1 (x) x +f2 (x) x2 +g(x) =0 ( 1)andadtainedmanyresultsonthequalitativebehaviorofequation ( 1) .FortheretardedLi啨nard typeequation¨x+f1 (x) x+f2 (x) x2 +φ(x) +g(x(t -h) ) =0 ,( 2 )wherehisanonnegativeconstant,f1 ,f2 ,φandgarecontinuousfunctionsonR ,theauthorsin [2 ]haveinvestigatedstabilityandbounde… 相似文献
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For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions. 相似文献
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对具有分布时滞的非自治Cohen-Grossberg神经网络进行了研究.通过构造适当的Lyapunov函数,利用不等式分析方法,引入多参数,得到了一系列解的一致有界性且最终有界性和全局指数稳定性的判别准则. 相似文献
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一类四阶非线性微分方程解的有界性及稳定性 总被引:11,自引:0,他引:11
运用Liapunov函数方法,研究了一类四阶非线性微分方程解的有界性及稳定性,得到了解的有界性及零解的全局渐近稳定性的充分条件。 相似文献
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本文研究了具有有限时滞中立型泛函微分方程解的有界性问题 ,得到了方程解的指数渐近稳定性蕴涵有界解的存在性的新的结果 相似文献
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一类高阶时滞差分方程的有界持久性与全局渐近稳定性 总被引:2,自引:0,他引:2
获得一类高阶时滞差分方程解的有界持久性和全局渐近稳定性的充分条件;所得结果部分地解决了G.Ladas的2个公开问题,推广了一些已知结果。 相似文献
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给出时滞 Lienard方程 x″+f( x) x′+ax′( t-τ) +g( x( t-τ) ) =0 ,a 0 ,一致有界及全局渐近稳定的充分条件 .讨论一阶导数项 ax′( t-τ)对方程有界性及渐近稳定性的影响 . 相似文献
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The stochastic theta method gives a computational procedure for simulating ordinary stochastic differential equations. The method involves a free parameter, . Here, we characterise the precise value of beyond which the region of linear asymptotic stability of the method becomes unbounded. The cutoff point is seen to differ from that in the deterministic case. Computations that suggest further results are also given. 相似文献
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Ulrich Krause 《Journal of Difference Equations and Applications》2013,19(4):343-356
Sufficient conditions are given under which the higher order difference equation x n+1= f(x n,x n-1,...,xn-k ), n=0,1,2,... generates an order preserving discrete dynamical system with respect to the discrete exponential ordering. It is shown that under the above monotonicity assumption the boundedness of all solutions as well as the local and global stability of an equilibrium hold if and only if they hold for the much simpler first order equation x n+1=h(x n ), where h(x)=f(x,x,…,x). As an application, a second order nonlinear difference equation from macroeconomics and a discrete analogue of a model of haematopoiesis are discussed. 相似文献
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应用能量估计方法和Gagliardo-Nirenberg型不等式,讨论了带自扩散和交错扩散的三种群Lotka-Volterra竞争模型解的一致有界性和整体存在性,并由Lyapunov函数证明了该模型正平衡点的全局渐近稳定性. 相似文献
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Sufficient conditions for boundedness and continuity are obtained for stochastically continuous infinitely divisible processes, without Gaussian component, {Y(t),t T}, where T is a compact metric space or pseudo-metric space. Such processes have a version given by Y(t)=X(t)+b(t),tT where b is a deterministic drift function and
Here N is a Poisson random measure on a Borel space S with –finite mean measure , and
is a measurable deterministic function. Let : T2 R+ be a continuous pseudo–metric on T. Define the -Lipschitz norm of the sections of f by
for some t0 T, where D is the diameter of (T,). The sufficient conditions for boundedness and continuity of X are given in terms of the measure
and majorizing measure and or metric entropy conditions determined by . They are applied to stochastic integrals of the form
where M is a zero-mean, independently scattered, infinitely divisible random measure without Gaussian component. Several examples are given which show that in many cases the conditions obtained are quite sharp. In addition to obtaining conditions for continuity and boundedness, bounds are obtained for the weak and strong Lp norms of
and
for all
. These results depend on inequalities for moments and related functions of the weak and strong
norms of sequences {xj}, which are the events of Poisson point process M on R+ and are given in terms of the intensity measure of M. These results are of independent interest. 相似文献
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Cheng-jianZhang GengSun 《计算数学(英文版)》2004,22(3):447-456
In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some criteria of the boundedness and the asymptotic stability for the methods are obtained. 相似文献
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BOUNDEDNESSANDBLOWUPFORTHEGENERALACTIVATOR-INHIBITORMODELLiMINGDE(李名德);CHENSHAOHUA(陈绍华);QINYUCHUN(秦禹春)(DepartmentofMathematic... 相似文献
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We consider the elliptic system , and an obstacle problem for a similar system of variational inequalities. The functions and satisfy certain ellipticity and boundedness conditions with a -admissible weight and exponent . The growth of in and is of order . We show that weak solutions of the above systems are locally bounded and differentiable almost everywhere in the classical sense.
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Connections between the spectral radius and the radius of boundedness are studied. Different characterizations of algebras (Q-property, strong saquentiality) are given in terms of these radii. Examples and applications are also provided. 相似文献