unbounded solutions of the equation asymptotic behavior of solutions of first order differential equation with deviating arguments in the email protected t email protected email protected i t y email protected i y email protected i is discussed for t a criterion for representing solutions in exponential form is proved inequalities for solution estimation are given sufficient conditions for the existence of unbounded solutions are derived a relevant illustrative example is given as well known results are discussed and compared

explicit exponential stability conditions for linear differential equations with several delays abstract new explicit conditions of exponential stability are obtained for the nonautonomous linear equation x t k 1 m a k t x h k t 0 where k 1 m a k t 0 h k t t by comparing this equation with a nonoscillatory exponentially stable equation of the form x t k i a k t x g k t 0 where i 1 m g k t t every comparison result gives 2 m 1 different stability conditions due to the a priori choice of a subset i

convergence to a constant of the solutions of differential equations with impulse effect abstract this paper examines the necessary and sufficient conditions for which the solutions of a system with impulse effect tend exponentially to a constant as t

statistical tests for multivariate bioequivalence although the u s food and drug administration fda 1992 recommends testing bioequivalence of individual pharmacokinetic parameters one at a time it seems reasonable and interesting to conduct a test simultaneously for all the parameters in this paper we discuss several ways to construct such tests it is shown that the confidence set approach leads to a test which can be uniformly improved by the intersection of schuirmann s two one sided tests procedure the latter test can further be improved upon noticeably by using the one dimensional unbiased test of brown hwang munk 1997 numerical calculations of powers are given to support this claim

3 2 stability conditions for a class of volterra levin equations abstract in this paper a generalized volterra levin equation is considered 3 2 stability conditions are established for ensuring that the zero solution of the equation is uniformly stable asymptotically stable and globally asymptotically stable further results are obtained under nonnegativity assumption the main results are new and different from the known results

perturbing uniformly stable nonlinear scalar delay differential equations on considere l equation differentielle a retard perturbee x t f t x t g t x t ou g o s r s x r x on donne des conditions sur g qui assurent que la solution zero est uniformement stable sous certaines conditions

simultaneous confidence regions for multivariate bioequivalence demonstrating bioequivalence of several pharmacokinetic pk parameters such as auc and cmax that are calculated from the same biological sample measurements is in fact a multivariate problem even though this is neglected by most practitioners and regulatory bodies who typically settle for separate univariate analyses we believe however that a truly multivariate evaluation of all pk measures simultaneously is clearly more adequate in this paper we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation some of them work well for idealised scenarios but break down when faced with real data challenges such as unknown variance and correlation among the pk parameters we study the shapes of the confidence regions resulting from different methods discuss how marginal simultaneous confidence intervals for the individual pk measures can be derived and illustrate the application to data from a trial on ticlopidine hydrochloride an r package is available

asymptotic stability for a linear difference equation with variable delay we shall obtain sufficient conditions for the uniform stability and the global asymptotic stability of the linear difference equation with variable delay xn 1 xn pnxn kn 0 n n where pn is a sequence of nonnegative real numbers kn is a sequence of nonnegative integers and there exists a nonnegative integer k such that kn k for n n

asymptotic theory for a class of nonautonomous delay differential equations this paper deals with asymptotic behavior of solutions of the nonlinear nonautonomous delay differential equation x t t r t t f t x s d t s su where xf t x 0 f t 0 0 t r t nondecreasing t s is nondecreasing and of bounded variation general sufficient conditions which are easy to verify are obtained for the solutions to be bounded and asymptotically stable locally and globally these results improve many existing ones principally by allowing i r t to be unbounded ii both discrete and distributed delays and iii the equation to be strongly nonlinear and nonautonomous various examples are given in the form of corollaries with a highly flexible integrand

asymptotic behavior of a differential equation with distributed delays abstract in this paper sufficient conditions are established for the asymptotical behavior of solutions of the delay differential equation x t f t x t g t x t with distributed form delays some applications are also given for the neutral differential equation with distributed delays

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

a generalization of the three dimensional bernfeld haddock conjecture and its proof consider the following system of delay differential equations x 1 t f x 1 t g x 2 t r 2 x 2 t f x 2 t g x 3 t r 3 x 3 t f x 3 t g x 1 t r 1 where r 1 r 2 and r 3 are positive constants f email protected c r 1 and f is nondecreasing on r 1 these systems have important practical applications and also are a three dimensional generalization of the bernfeld haddock conjecture in this paper by using comparative technique we obtain the asymptotic behavior of solutions that each bounded solution of the systems tends to a constant vector under a desirable condition

global attractivity for scalar differential equations with small delay abstract for scalar functional differential equations x t f t x t we refine the method of yorke and 3 2 type conditions to prove the global attractivity of the trivial solution the results are applied to establish sufficient conditions for the global attractivity of the positive equilibrium of scalar delayed population models of the form x t x t f t x t and illustrated with the study of two food limited population models with delay for which several criteria for their global attractivity are given

uniform asymptotic stability for perturbed neutral delay differential equations abstract one dimensional perturbed neutral delay differential equations of the form x t p t x t f t x t g t x t are considered assuming that f satisfies v t m f t v t m where m max 0 max s r 0 s a typical result is the following if g t w t and t t 1 w s ds 0 then the zero solution is uniformly asymptotically stable providing that the zero solution of the corresponding equation without perturbation x t p t x t f t x t is uniformly asymptotically stable some known results associated with this equation are extended and improved

preservation of stability in delay equations under delay perturbations we consider a class of linear delay equations with perturbed time lags and present conditions which guarantee that the asymptotic stability of the trivial solution of the equation at hand is preserved under these perturbations as an example we show how our results can be used to obtain an estimate on the maximum allowable sampling interval in the stabilization of a hybrid system with feedback delays we also present applications of our perturbation theorem to obtain stability conditions for delay equations with multiple delays

uniform asymptotic stability in perturbed differential equations on etudie la stabilite asymptotique uniforme de la solution zero des equations differentielles perturbees x f t x g t x et si t f t x t g t x t

asymptotic convergence criteria of solutions of delayed functional differential equations abstract the convergence of all solutions of the scalar equation x f t x t is studied under the main assumption that every constant is its solution the criterion and the sufficient conditions for convergence are proved for the considered classes of equations it is among others proved that all solutions are convergent if and only if there exists at least one increasing and convergent solution as applications criteria for some classes of linear equations as well as for nonlinear equations are obtained some comparisons with already known results are given too

asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients abstract sufficient conditions are established for the asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients x t p t x t q 1 t x t 1 q 2 t x t 2 0 t t 0 where 1 2 0 p q 1 q 2 c t 0 r some known results are generalized and improved

sobolev s inequalities and vanishing integrability for riesz potentials of functions in the generalized lebesgue space lp logl q abstract our aim in this paper is to deal with sobolev s inequalities for riesz potentials of functions belonging to l p log l q to do so we study the boundedness of hardy littlewood maximal functions and apply the hedberg s trick as an application we treat vanishing integrability for riesz potentials

bayesian modeling of multivariate average bioequivalence bioequivalence trials are usually conducted to compare two or more formulations of a drug simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence despite the fact that some tests for multivariate bioequivalence are suggested current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as auc and cmax in this paper we develop a semiparametric bayesian test for bioequivalence under multiple endpoints specifically we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference resulting estimates and posterior probabilities borrow strength from one another where the amount and the direction of the strength borrowed are determined by the prior correlations the method developed is illustrated using a real data set copyright 2007 john wiley sons ltd

convergence of the solutions of the equation y t β t y t δ y t τ in the critical case we study the asymptotic behavior of the solutions of the first order differential equation containing two delays y t t y t y t with t0 r 0 the convergence of all solutions is characterized by the existence of a strictly increasing bounded solution a critical case is found for the coefficient function for coefficients below the critical function a strictly increasing and bounded solution is constructed and thus the convergence of all solutions is shown relations with known results are discussed too

asymptotic representation of solutions of equationẏ t β t y t y t τ t abstract in this paper the equation t t y t y t t is considered where c i 1 r i 1 t 1 r 0 t t is an increasing function on i 1 t t i 1 0 c i 1 r results about asymptotic structure and behavior of the solutions of this equation are proved a connection with the equation t c t x t t and the asymptotic representation of its solutions is obtained

existence and global attractivity of periodic solution for an impulsive delay differential equation with allee effect sufficient conditions are obtained for the existence and global attractivity of positive periodic solution of an impulsive delay differential equation with allee effect the results of this paper improve and generalize noticeably the known theorems in the literature

solution estimates for linear differential equations with delay abstract in this paper we give explicit exponential estimates x t m e t t 0 where t t0 m 0 for solutions of a linear scalar delay differential equation x t k 1 m b k t x h k t f t t t 0 x t t t t 0 we consider two different cases when 0 corresponding to exponential stability and the case of in the first case together with the exponential estimate we also obtain an exponential stability test in the second case we get estimation for solution growth here both the coefficients and the delays are measurable not necessarily continuous

unbounded increasing solutions of a system of difference equations with delays we consider a homogeneous system of difference equations with deviating arguments in the form y n k 1 q k n y n p k y n r k where n n 0 n 0 z p k r k are integers r k p k 0 q is a positive integer y y 1 y s t y n 0 r n 0 r 1 r s is an unknown discrete vector function s 1 is an integer r max r 1 r q y n y n 1 y n and k n ij k n i j 1 s are real matrices such that ij k n 0 n 0 1 0 and k 1 q j 1 s ij k n 0 for each admissible i and all n n 0 the behavior of solutions of this system is discussed for n the existence of unbounded increasing solutions in an exponential form is proved and estimates of solutions are given the scalar case is discussed as well

asymptotic integration of delay differential systems on considere des equations non autonomes qui sont asymptotiquement autonomes et on cherche des formules pour les solutions aux grandes valeurs de la variable independante

global attractivity in scalar delayed differential equations with applications to population models for the scalar delay differential equation x t 1 x t f t xt sufficient conditions for the global stability of the zero solution are given the behavior of global solutions on r is also addressed several applications to population models which improve known results are presented

convergence of a class of discrete time semiflows with application to neutral delay differential equations abstract in this paper we introduce a class of pseudo monotone maps on ordered topological spaces by exploiting monotonicity methods and the invariance of the omega limit set we establish a convergence principle for discrete time semiflows generated by the maps introduced the convergence principle is then applied to a class of periodic neutral delay differential equations which leads to some novel and sharper results

stability of a pure random delay system with two time scale markovian switching abstract this work examines almost sure stability of a pure random delay system whose delay time is modeled by a finite state continuous time markov chain with two time scales the markov chain contains a fast varying part and a slowly changing part using the properties of the weighted occupation measure of the markov chain it is shown that the overall system s almost sure asymptotic stability can be obtained by using the averaged delay this feature implies that even if some longer delay times may destabilize the system individually the system may still be stable if their impact is balanced in other words the markov chain becomes a stabilizing factor numerical results are provided to demonstrate our results

exponential solutions of equation ẏ t β t y t δ y t τ abstract asymptotic behaviour of solutions of first order differential equation with two deviating arguments of the form y t t y t y t is discussed for t a criterion for representing solutions in exponential form is proved as consequences inequalities for such solutions are given connections with known results are discussed and a sufficient condition for existence of unbounded solutions generalizing previous ones is derived an illustrative example is considered too

asymptotic behavior of certain delay differential equations with forcing term abstract we study the asymptotic behavior of solutions of the following forced delay differential equation x t p t f x t r t t 0 some sufficient conditions that guarantee every solution of the equation to converge to zero are obtained the results obtained are applied to some well known delay differential ecological equations with forcing term

stability criteria of differential systems via liapunov s second method stability notions for systems of ordinary and functional differential equations were investigated by many authors our purpose in this paper is to study sufficient conditions of different types of stability and improvements of some results of athanassov yoneyama and li fu furthermore we show that the condition v t 0 0 is not sometimes a necessary condition for stability results

in vitro bioequivalence testing a statistical test is proposed for in vitro bioequivalence testing between drug products such as nasal aerosols and nasal sprays the proposed test generalizes the one recommended in the fda 1999 guidance to the situation where replicated observations obtained from each sampled canister or bottle of the drug product are available the technique developed by hyslop hsuan and holder is used so that the proposed test is asymptotically accurate the type i error probability and power of the proposed test are investigated through a simulation study a method for determining the required sample size to achieve a desired power is also proposed a numerical example is given for illustration

differentiability properties of functions from higher order orlicz sobolev spaces abstract we analyze pointwise differentiability properties of functions from local orlicz sobolev spaces w loc m a on an open subset of r n n 2 a necessary and sufficient condition on the order of differentiation m and on the young function a is exhibited for any function in w loc m a to admit a differential of order m a e in an optimal approximate differentiability property in integral and norm form is established when such a condition fails

stability in n dimensional delay differential equations abstract in this paper we give some sufficient conditions for the zero solution of an n dimensional delay differential equation of the form x t a t x t t x t t 0 to be uniformly stable and asymptotically stable these conditions extend and improve the existing relative results in literature

capacity for potentials of functions in musielak orlicz spaces abstract we define a capacity for potentials of functions in musielak orlicz spaces basic properties of such capacity are studied we also estimate the capacity of balls and give some applications of the estimates

stability on nonlinear delay differential equations with impulses abstract in this paper the asymptotic stability for nonlinear delay differential equations with impulses 1 1 x t f t x t t 0 t t k x t k x t k i k x t k k n is studied and 3 2 stability theorems are presented the results here have improved the known results

bayesian multiple testing for two sample multivariate endpoints dans les essais cliniques ou l on s interesse a plusieurs variables il arrive souvent que des tests simultanes portent sur des resultats correles entre eux et concernent des hypotheses elles meme correlees entre elles cet article dans un cadre bayesien propose d utiliser comme loi de probabilite a priori des effets traitement une distribution multivariee ou la combinaison des parametres permet simultanement d affecter une probabilite strictement positive a l absence d effet traitement pour chacune des hypotheses et de modeliser differents types de correlations la correlation entre les effets traitements standardises c est a dire rapportes aux ecarts types des variables concernees la correlation entre les variables dichotomiques de presence ou d absence de l effet traitement la correlation enfin entre les statistiques de test conditionnellement aux effets reels nous developpons ensuite dans le cas de l etude multivariee de deux echantillons une methode de comparaisons multiples qui nous permet de calculer pour des variables prealablement specifiees les probabilites a posteriori d une absence d effet traitement sont aussi discutees dans le contexte d un exemple clinique reel les demarches relatives au choix de la probabilite a priori ainsi que les problemes de robustesse

stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients abstract we consider the following nonlinear impulsive delay differential equation with variable coefficients and forcing term x t a t x t f t x e t t 0 t t k x t k x t k i k x t k k n using new methods different from those in tang et al appl math comput 131 2002 373 nieto j comput appl math lett 15 2002 489 franco and nieto j comput appl math 88 1998 144 nieto j math anal appl 205 1997 423 he and yu j math anal appl 272 2002 67 we establish stability theorems for when e t 0 under the assumption that there is bk such that bkx2 x x ik x x2 for k n and x r theorems 2 1 2 4 the existence results for three positive periodic solutions and nonexistence results for periodic solution of when e t 0 under the assumption exp 0 t a u d u 0 t k 1 b k and bk 1 for all k theorems 3 1 3 2 and the existence results for periodic solution of at resonance which is caused by impulses i e exp 0 t a u d u 0 t k 1 b k under the assumption bk 1 for all k theorems 4 2 4 3 some results obtained improve and generalize the known theorems and some other results are new examples are presented to illustrate the main results

estimates for certain orlicz sobolev capacities of an euclidean ball abstract we calculate certain orlicz sobolev capacities of an euclidian n dimensional ball

global stability for separable nonlinear delay differential equations consider the following separable nonlinear delay differential equation dy t dt i 0ma i t g i y t i t t t 0y t f t t t 0 where we assume that there is a strictly monotone increasing function f x on such that f 0 0 00 0 i m andiff x x thenlim x f x orlim x f x isfinite in this paper to the above separable nonlinear delay differential equation we establish conditions of global asymptotic stability for the zero solution in particular for a special wide class of f x which contains a case of f x e x 1 we give more explicit conditions applying these we offer conditions of global asymptotic stability for solutions of nonautonomous logistic equations with delays

1 α equivariant confidence rules for convex alternatives are α 2 level tests with applications to the multivariate assessment of bioequivalence abstract in general a 1 confidence region c x for a parameter yields a test at level a for h h versus k c h whenever we reject if c x h we show under certain equivariance properties of c x that for the case of convex alternatives c h the level of the resulting test is in fact 2 this extends recent findings for hyperrectangular alternatives as they occur in the multivariate bioequivalence problem furthermore we apply the suggested test to ellipsoid type alternatives instead of hyperrectangulars in the multivariate bioequivalence problem and to a problem occurring in neurophysiology finally we compare our test numerically with existing methods

fixed points and stability in differential equations with variable delays abstract in this paper we consider a linear scalar differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic stability theorem with a necessary and sufficient condition is proved

growth properties of musielak orlicz integral means for riesz potentials abstract in this paper we are concerned with growth properties of integral means for riesz potentials of variable order of functions in musielak orlicz spaces l r n where is a function of the form x t t p x x t here and p satisfy the log holder condition we also discuss the size of the exceptional sets using a capacity introduced in maeda et al 2011

asymptotic stability in perturbed delay difference systems abstract consider the delay difference system x i n 1 x i n b i x i n l i n j 1 m d i j n x j n h i j n i j 1 2 m where 0 l i n l i 0 h i j n h i j d i j n d i j l i h i j are nonnegative integers b i 0 d i j 0 are real constants it is shown that the trivial solution of the above system is asymptotically stable if b i l i 1 3 2 1 2 l i 1 i 1 2 m and a certain matrix derived from the coefficient matrix is a nonsingular m matrix

convergence theorems and asymptotic integration for functional differential equations abstract this paper is devoted to the investigation on convergence of solutions and asymptotic integration of some functional differential equations fdes in the first part of the paper some convergence criteria are obtained and an invariance principle is established for the convergence of solutions of linear fdes under perturbations and disturbances with l 1 integrable coefficients these theorems are applicable to some nonlinear or nonhomogeneous equations in the second part the convergence theorems are applied to investigate the asymptotic integration of some linear fdes this research is made mainly to discuss a situation that was avoided by some previous literature some examples are given to illustrate the theorems

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

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

global attractivity of non autonomous lotka volterra competition system without instantaneous negative feedback abstract we consider a non autonomous lotka volterra competition system with distributed delays but without instantaneous negative feedbacks i e pure delay systems we establish some 3 2 type and m matrix type criteria for global attractivity of the positive equilibrium of the system which generalise and improve the existing ones

a semi parametric bayesian approach to average bioequivalence bioequivalence assessment is an issue of great interest development of statistical methods for assessing bioequivalence is an important area of research for statisticians bioequivalence is usually determined based on the normal distribution we relax this assumption and develop a semi parametric mixed model for bioequivalence data the proposed method is quite flexible and practically meaningful our proposed method is based on a mixture normal distribution and a non parametric bayesian approach using a dirichlet process mixture prior a numerical example illustrates the use of our procedure

stability of nonlinear delay differential equations with impulses abstract by relaxing the restriction used previously we obtain the improved 3 2 stability theorems for the nonlinear delay differential equations with impulses x t f t x t 0 t t k 1 1 x t k x t k i k x t k k n

stability for impulsive delay differential equations abstract in this paper the stability for the scalar impulsive delay differential equation y t a t y t f t y 0 t 0 t k y k y k i k y k k 1 2 lim k k where delay arguments may be bounded or unbounded is investigated some new stability theorems are established which improve and extend several known results in the literature

stability for first order delay dynamic equations on time scales in this paper we establish some sufficient conditions for the uniform stability and the uniformly asymptotical stability of the first order delay dynamic equation x d t p t x t t t 0 t t where t is a time scale p is rd continuous and positive the delay function t t 0 r our results unify the corresponding ones for differential and difference equations to the best of our knowledge this is the first time to discuss the asymptotical behavior of delay dynamic equations on time scales

compact embeddings in the generalized sobolev space w01 p g and existence of solutions for nonlinear elliptic problems abstract our aim in this paper is to deal with the compact embedding in the generalized sobolev space w 0 1 p g with a variable exponent satisfying the log holder condition as an application we find a nontrivial weak solution of the nonlinear elliptic problem div u x p x 2 u x f x u x in g u x 0 on g which is an extension of fan zhang x fan g h zhang existence of solutions for p x laplacian dirichlet problem nonlinear anal 52 2003 pp 1843 1852 theorem 4 7

stability conditions for scalar delay differential equations with a non delay term abstract the problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non autonomous equations which include a non delay term and one or more delayed terms first we demonstrate that introducing a non delay term with a non negative coefficient can destroy stability of the delay equation next sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained the nonlinear results are applied to the mackey glass model of respiratory dynamics

vanishing exponential integrability for functions whose gradients belong to ln log e l α if the gradient of u x is nth power locally integrable on euclidean n space then the integral average over a ball b of the exponential of a constant multiple of u x ub n n 1 ub average of u over b tends to 1 as the radius of b shrinks to zero for quasi almost all center points this refines a result of n trudinger 1967 we prove here a similar result for the class of gradients in ln log e l 0 n 1 the results depend on a capacitary strong type inequality for these spaces

asymptotic behavior of delay differential equations with instantaneously terms abstract this paper deals with scalar delay differential equation with instantaneously term x t cr t x t f t x t 0 sharp sufficient conditions are obtained for the asymptotic behavior of solutions when c 1

a global stability criterion in nonautonomous delay differential equations abstract consider the following nonautonomous nonlinear delay differential equation d y t d t a t y t i 0 m a i t g i y i t t t 0 y t t t t 0 where we assume that there is a strictly monotone increasing function f x on such that f 0 0 0 g i x f x 1 x 0 0 i m and if f x x then lim x f x or lim x f x is finite in this paper to the above nonautonomous nonlinear delay differential equation we establish conditions of global asymptotic stability for the zero solution in particular for a special wide class of f x which contains two cases f x e x 1 and f x x we give more explicit conditions which are some extension of the 3 2 type criterion applying these to discrete models of nonautonomous delay differential equations we also obtain new sufficient conditions of the global asymptotic stability of the zero solution

on the stability region of scalar delay differential equations on considere l equation differentielle scalaire a retard x t x t x t q ou r et q 0 on definit les regions de stabilite des solutions

positive solutions of the equation ẋ t c t x t τ in the critical case abstract the equation t c t x t is considered in the critical case for it the asymptotic behavior of dominant and subdominant solutions is studied a generalization is made and connections with known results are discussed

stability theorem for a class of nonautonomous neutral differential equations with unbounded delay consider the one dimensional nonautonomous neutral differential equation ddt xt ft xpt gt xqt 0 t t0 where p q t0 r are continuous and strictly increasing p t t q t t for all t t0 and xg t x 0 for t t0 x r in this paper the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable

convergence in asymptotically autonomous functional differential equations in this paper we consider linear and nonlinear perturbations of a linear autonomous functional differential equation which has infinitely many equilibria we give sufficient conditions under which the solutions of the perturbed equation tend to the equilibria of the unperturbed equation at infinity as a consequence we obtain sufficient conditions for systems of delay differential equations to have asymptotic equilibrium

convergence of bounded solutions for a class of systems of delay differential equations abstract in this paper the convergence of a class of systems of delay differential equations is considered we show that every bounded solution of such systems tends to an equilibrium under certain hypotheses our results extend some corresponding ones already known