p moment stability of functional differential equations with random impulses by means of liapunov s direct method coupled with razumikhin technique some sufficient conditions for uniform uniform and globally asymptotic uniformly globally asymptotic and globally exponential p moment stability of the zero solution of functional differential equations with random impulses are presented where the parameter l t in dv t x t dt is not required to be negative definite thus the obtained results are convenient to apply

stability theorem for delay differential equations with impulses abstract in this paper we obtain sufficient conditions for the stability of the zero solution of the delay differential equation with impulses formula

on model complete differential fields we develop a geometric approach to definable sets in differentially closed fields with emphasis on the question of orthogonality to a given strongly minimal set equivalently within a family of ordinary differential equations we consider those equations that can be transformed by differential algebraic transformations so as to yield solutions of a given fixed first order ode x we show that this sub family is usually definable in particular if x lives on a curve of positive genus as a corollary we show the existence of many model complete superstable theories of differential fields

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

generalized scalar curvature type equations on compact riemannian manifolds the paper is concerned with nonlinear equations of critical sobolev growth involving the p laplace operator these equations generalize the more classical scalar curvature equation

exponential stability of functional differential systems with impulsive effect on random moments abstract the model of nonlinear functional differential systems with impulsive effect on random moments is brought forward by authors in this paper then by means of liapunov s direct method coupled with razumikhin technique and comparison principle sufficient conditions for p moment exponential stability of the trivial solution to the systems are present where the parameter t in dv t x t dt are not required to be negative finally an example is discussed to show the applications of the obtained results

the existence and exponential stability of semilinear functional differential equations with random impulses under non uniqueness a b s t r a c t in this paper the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non uniqueness in a real separable hilbert space the results are obtained by using the leray schauder alternative fixed point theorem

the nonoscillatory solutions of delay differential equations with impulses abstract we obtain a sufficient condition for the impulsive delay differential equation t i 1 n p i t r i t t t k t k t k i k t k k n to have a nonoscillatory solution

on algebraic relations between solutions of a generic painleve equation we prove that if y 00 f y y 0 t is a generic painlev e equation that is an equation in one of the families pi pv i but with the relevant complex parameters algebraically independent and if y1 yn are solutions such that y1 y 0 y2 y 0 yn y 0 n are algebraically dependent over c t then already for some 1 i j n yi y 0 yj y 0 are algebraically dependent over c t the proof combines results by the japanese school on irreducibility of the painlev e equations with the trichotomy theorem for strongly minimal sets in dierentially closed elds

finiteness theorems on hypersurfaces in partial differential algebraic geometry abstract hrushovski s generalization and application of jouanolou 1978 9 is here refined and extended to the partial differential setting with possibly nonconstant coefficient fields in particular it is shown that if x is a differential algebraic variety over a partial differential field f that is finitely generated over its constant field f 0 then there exists a dominant differential rational map from x to the constant points of an algebraic variety v over f 0 such that all but finitely many codimension one subvarieties of x over f arise as pull backs of algebraic subvarieties of v over f 0 as an application it is shown that the algebraic solutions to a first order algebraic differential equation over c t are of bounded height answering a question of eremenko two expected model theoretic applications to dcf 0 m are also given 1 lascar rank and morley rank agree in dimension two and 2 dimension one strongly minimal sets orthogonal to the constants are 0 categorical a detailed exposition of hrushovski s original unpublished theorem is included influenced by ghys 2000 5

harnack estimates for a heat type equation under the ricci flow abstract in this paper we consider the gradient estimates for a positive solution of the nonlinear parabolic equation t u t u h u p on a riemannian manifold whose metrics evolve under the ricci flow two harnack inequalities and other interesting results are obtained

stability under persistent disturbances of impulsive differential difference equations of neutral type abstract effective sufficient conditions for stability under persistent disturbances of the zero solution of impulsive systems of differential difference equations of neutral type are found the main results are stated in a theorem in its proof an analogue of gronwall bellman s inequality for piecewise continuous functions is used as a corollary the existence of a global solution of a system with quadratic nonlinearities is proved for sufficiently small initial data

liouvillian first integrals of differential equations liouvillian functions are functions that are built up from rational functions using exponentiation integration and algebraic functions we show that if a system of differential equations has a generic solution that satisfies a liouvillian relation that is there is a liouvillian function of several variables vanishing on the curve defined by this solution then the system has a liouvillian first integral that is a nonconstant liouvillian function that is constant on solution curves in some nonempty open set we can refine this result in special cases to show that the first integral must be of a very special form

the persistence of nonoscillatory solutions of delay differential equations under impulsive perturbations abstract we obtain a sufficient condition for the persistence of nonoscillatory solutions of the delay differential equation under impulsive perturbations

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

stability of the zero solution of impulsive differential equations by the lyapunov second method abstract the paper is concerned with the stability of the zero solution of the impulsive system dx dt f t x t i x x t i x j i x i n 1 2 where x t x x x limt x t the lyapunov second method is used as a tool in obtaining the criteria for stability asymptotic stability and instability of the trivial solution

stability analysis of complex valued impulsive systems with time delay in this paper the global exponential stability of complex valued impulsive systems is addressed some new sufficient conditions are obtained to guarantee the global exponential stability by the lyapunov razumikhin theory which extend and improve most of recent results moreover the obtained razumikhin conditions are very simple and efficient to verify in real problems and helpful to investigate the stability of delayed neural networks and synchronization problems of chaotic systems under impulsive perturbation finally a numerical example is given to show the effectiveness of the obtained results

new razumikhin type theorems for impulsive functional differential equations in this paper we investigate stability and boundedness for a class of impulsive functional differential equations by using liapunov functions and razumikhin technique some new razumikhin type theorems on stability and boundedness are obtained the corresponding results obtained recently in j shen j yan nonlinear anal 33 1998 519 531 x liu j shen to appear are improved

oscillation stability and boundedness of second order differential systems with random impulses the model of second order linear differential systems with random impulses is brought forward in this paper then necessary and sufficient conditions for oscillation in mean p moment stability and p moment boundedness are obtained by several theorems that compare solutions of this system with the corresponding nonimpulsive differential system at last an example is presented to show the application of obtained results

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

convergence rate of the fuzzy generalized nearest neighbor rule tizzy k nearest neighbor rule k nnr has been applied in a variety of substantive areas yang and chen l described a fuzzy generalized k nn algorithm which is a unified approach to a variety of fuzzy k nnr s they created the strong consistency of posterior risk of the fuzzy generalized nnr in this paper we give their convergence rate that is the convergence rate of posterior risk of the fuzzy generalized nnr is exponentially fast

lyapunov razumikhin method for impulsive functional differential equations and applications to the population dynamics the present paper deals with the investigation of the stability of the zero solution of impulsive functional differential equations by means of piecewise continuous functions coupled with the razumikhin technique sufficient conditions for stability uniform stability and asymptotic stability of the zero solution of such equations are found

impulsive stabilization of functional differential equations via liapunov functionals abstract in this paper we consider the impulsive stabilization problems for a class of impulsive functional differential equation of the form x t f t x t t t 0 x i k t x t t t k k z our method is based on the application of the liapunov second method together with liapunov functionals

asymptotic behavior of solutions of nonlinear neutral differential equations with impulses abstract this paper is concerned with a nonlinear neutral differential equations with impulses of the form x t c t x t p t f x t 0 t t 0 t t k x t k b k x t k 1 b k t k t k p s f x s d s k 1 2 sufficient conditions are obtained for every solution of and that tends to a constant as t

hybrid stabilization and synchronization of nonlinear systems with unbounded delays the stabilization of nonlinear systems with bounded and unbounded time delays via hybrid control is studied we investigate and identify switching rules for which stabilization can be verified a priori when this approach is inadequate stabilizing state dependent switching rules are constructed this method is based on partitioning the state space into switching regions unwanted physical behavior such as chattering and zeno behavior is avoided sufficient conditions are established using razumikhin like theorems the theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay the findings are illustrated through numerical simulations

liouville theorem for weighted p lichnerowicz equation on smooth metric measure space abstract in this paper let m n g d be n dimensional noncompact metric measure space which satisfies poincare inequality with some ricci curvature condition we obtain a liouville theorem for positive weak solutions to weighted p lichnerowicz equation p f v c v 0 where c 0 m n 1 1 p m 1 m 1 m 3 2 p 1 are real constants

on stability of perturbed impulsive differential systems the notion of lipschitz stability of impulsive systems of differential equations des was introduced in this paper we will extend the notion of eventual stability to impulsive systems of des and extend the notion of lipschitz stability of impulsive systems of des to a new type of stability called eventual lipschitz stability some criteria and results are given our technique depends on liapunov s direct method and comparison principle

asymptotic behavior of solutions of impulsive delay differential equations abstract effective sufficient conditions for the asymptotic stability of the trivial solution of impulsive delay differential equation formula are obtained by investigating respectively the asymptotic behavior of the nonoscillatory solutions and oscillatory solutions of the equation