On the pth moment exponential stability criteria of neutral stochastic functional differential equations

The paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the Ito type. This investigation can be very complicated, even in many special cases, by using usual methods based on Lyapunov functionals. In this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations.     

奇摄动非线性边值问题

§ 1 .　Introduction　　AclassofintegraldifferentialequationsDirichletboundaryvalueproblemsforordinarydif ferentialequationandellipticequationarediscussedin [1]and [2 ]respectively .Andin [3]akindofnonlocalproblemsforsingularlyperturbedreactiondiffusionsystemsarestudied.Inthispaper,whatisworthpointingoutisaclassofnonlinearboundaryvalueproblemsdiscussed,applyingthemethodofcompositeexpandandthetheoryofdifferentialinequalities.εy″ =f(x ,y ,Tεy ,ε) y′ +g(x ,y ,Tεy,ε) ,0 相似文献   

单层介质膜保偏全反射直角三棱镜镀膜材料的选择及其微分相位特性研究

入射角、基底玻璃折射率、膜介质折射率、膜厚等因素会影响单层介质膜保偏全反射直角三棱镜的保偏特性，且各因素的影响程度并不相同。本文分析了上述各因素的微小变化对保偏特性的影响，并提出了选择膜介质的方法     

An Oscillation Criterion for Second Order Superlinear Differential Equations

61.IntroductionConsiderthesecondordersuperlinearequationx'(t) p(t)X'(t) q(t)1x(t)l"sgnx(t)=o,t>to,(1)wherea>l,pandq:[t,'co)-R=(-co,oo)arecontinuous.Weconsideronlysuchsolutionsxofequation(l)whichexistonsomeinterval[t.,oo),t.>t,>o.Asolutionofequation(l)issaidtobeoscillatoryifithasarbitrarilylargezerosandotherwise,itissaidtobenonoscillatory.Equation(l)iscalledoscillatoryifallofitssolutionsareoscilllatory.Forthespecialcasewherep(t)=Oli.e.,forthedifferentialequationx'(t) q(t)lx(t)l"sgnx(t)=o,a>1-…     

中立型抛物方程解的强迫振动性

本文讨论中立型抛物方程解的强迫振动，其中Ω是Rn中具有光滑边界Ω的有界区域，     

Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions

In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on y, with Lipschitz condition on z.     

Radiative transfer in absorbing, emitting and linearly anisotropic-scattering inhomogeneous cylindrical medium

Radiative integral transfer equations for one-dimensional solid cylinder with absorbing, emitting and linearly anisotropic-scattering inhomogeneous medium were derived by Abulwafa et al. (JQSRT 62 (1999) 755). The anisotropic terms in the integral equations and their results for anisotropic benchmark problems (JQSRT 66 (2000) 487) are inaccurate. In this study, the integral equations for absorbing, emitting and linearly anisotropic-scattering medium are rederived, and the integral equations for one-dimensional solid cylindrical medium are solved. The results are compared with selected cases using the discrete ordinates S₁₆ and the exact solutions available in the literature.     

Monitoring cooperative equilibria in a stochastic differential game

This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.This research was supported by FNRS-Switzerland, NSERC-Canada, FCAR-Quebec.     

ON THE BOUNDEDNESS OF A CERTAIN SYSTEM OF FIFTH-ORDER DIFFERENTIAL EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｓｈａｌｂｅｃｏｎｃｅｒｎｅｄｈｅｒｅｗｉｔｈｒｅａｌｆｉｆｔｈｏｒｄｅｒｖｅｃｔｏｒｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｔｈｅｆｏｒｍ：Ｘ（５）＋Ｆ（Ｘ．．）Ｘ（４）＋Φ（Ｘ．．）＋Ｇ（Ｘ．．）＋Ｈ（Ｘ．）＋Ψ...     

Logarithmic Norms and Nonlinear DAE Stability

Logarithmic norms are often used to estimate stability and perturbation bounds in linear ODEs. Extensions to other classes of problems such as nonlinear dynamics, DAEs and PDEs require careful modifications of the logarithmic norm. With a conceptual focus, we combine the extension to nonlinear ODEs [15] with that of matrix pencils [10] in order to treat nonlinear DAEs with a view to cover certain unbounded operators, i.e. partial differential algebraic equations. Perturbation bounds are obtained from differential inequalities for any given norm by using the relation between Dini derivatives and semi-inner products. Simple discretizations are also considered.