an elliptic parabolic free boundary problem continuity of the interface on etablit la continuite de l interface de la solution faible d un probleme elliptique parabolique lie a la theorie des ecoulements partiellement satures dans les milieux poreux on utilise une methode basee sur le principe du maximum pour les equations paraboliques en supposant l ecoulement unidimensionnel

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 scalar extensions and spectral decompositions of complex symmetric operators abstract in this paper we prove that a complex symmetric operator with property is subscalar as a corollary we get that such operators with rich spectra have nontrivial invariant subspaces we also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints

the improvement of razumikhin type theorems for impulsive functional differential equations abstract in this paper by using lyapunov functions and razumikhin techniques the stability of impulsive functional differential equations is investigated the obtained results avoid the difficulty of constructing a p function in razumikhin s condition and they generalize and improve the existing theorems an example is given to illustrate the importance of the obtained results

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

on the existence of periodic solutions of a neutral delay model of single species population growth abstract in this paper we employ some new techniques to study the existence of positive periodic solutions of the neutral delay model n t n t a t t n t b t n t t c t n t t our result gives a correct answer to the open problem 9 2 due to y kuang 1993 delay differential equations with applications in population dynamics academic press new york

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

high order runge kutta methods for impulsive delay differential equations abstract the purpose of this paper is to obtain high order runge kutta methods for nonlinear impulsive delay differential equations iddes in order to achieve the purpose continuity and smoothness of the exact solutions of iddes are analyzed and then the discontinuous points and non smooth points are chosen as a part of the nodes of the runge kutta methods furthermore it is proved that the pth order runge kutta method for iddes is also convergent of order p and some simple numerical examples are given to demonstrate the theoretical results

new razumikhin type theorems on the stability for impulsive functional differential systems in this paper we investigate the stability of the trivial solution for impulsive functional differential systems using several lyapunov functions including partial components coupled with the razumikhin technique and obtained some new razumikhin type theorems which avoid using the auxiliary function p under less restrictive conditions our results improve some of the earlier findings and are suitable for many applications some examples are given to illustrate the advantages of the theorems obtained

existence of positive periodic solutions for neutral population model with multiple delays in this paper the authors employ an abstract continuous theorem of k set contractive operator and some analysis techniques to study the existence of positive periodic solutions for a neutral delay population model with multiple delays as followsdndt n t a t b t n t j 1 nb j t n t s i t i 1 mc i t n t t i t a new result on the existence of positive periodic solutions is obtained

existence of positive periodic solutions of a neutral delay lotka volterra system with impulses sufficient conditions are obtained for the existence of periodic positive solutions of a class of neutral impulsive delay lotka volterra systems n i t n i t a i t j 1n b i j t n j t t i j t j 1nc i j t n j t c i j t n i t k n i t k b i kn i t k i 1 2 n k 1 2 by using some techniques of mawhin coincidence degree theory my results generalize some known results it is shown that under the appropriate linear periodic impulsive perturbations the neutral impulsive delay lotka volterra system preserves the original periodicity of the neutral nonimpulsive delay lotka volterra system

further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations abstract this paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations x t a t x t f t x t x 1 t x n t t j t 1 t p x t k x t k i k x t k k 1 2 p x 0 x t we obtain sufficient conditions for the existence of at least one solution of problem at resonance and nonresonance cases respectively examples are presented to illustrate the main results

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 m complex symmetric weighted shift operators on cn abstract in this paper we study m complex symmetric weighted shift operators on c n let t be the backward weighted shift on c n for some n 2 we consider when t and t a the matrix of entries the moduli of those of t are both m complex symmetric with the same standard conjugation c give as well some unitary operators useful in the study and generalize to upper triangular matrices also we show that if t is 2k complex symmetric with the standard conjugation c for some k n with k n then t is 2 k 1 complex symmetric with the conjugation c

a new approach to stability of impulsive functional differential equations in this work a new approach to stability theory of impulsive functional differential equations is proposed instead of putting all components of the state variable x in one liapunov function several functions of partial components of x which can be much easier constructed are used so that the conditions ensuring that stability are simpler and less restrictive also an example is given to illustrate the advantages of the obtained results

on local spectral properties of complex symmetric operators abstract in this paper we study properties of complex symmetric operators in particular we prove that every complex symmetric operator having property or is decomposable moreover we show that complex symmetric operator t has dunford s property c and it satisfies weyl s theorem if and only if its adjoint does

existence of positive periodic solutions for a neutral population model with delays and impulse in this paper by using the theory of abstract continuous theorem of k set contractive operator and some analysis techniques we obtain some sufficient conditions for the existence of positive periodic solutions for a neutral population model with delays and impulse

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

stability of nontrivial solution of delay differential equations with state dependent impulses this paper considers the stability problem of nontrivial solutions of delay differential equations with state dependent impulses by using the concepts of reduced system and quasi stability the stability problem of a nontrivial solution of the impulsive delay differential equation with state dependent impulses is converted to that of the trivial solution of the impulsive delay differential equation with fixed impulses several stability criteria are then established utilizing the known results for systems with fixed impulses

stability theory of hybrid dynamical systems with time delay by defining the bounded time lag space and other related concepts this note formulates the notion of hybrid dynamical systems with time delay which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis it also investigates stability properties of invariant sets by the method of lyapunov functions and the razumihin techniques criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with time delay those criteria are then applied to conduct stability analysis for impulsive delay differential systems and nonlinear sampled data feedback control systems with time delay

on complex symmetric operator matrices abstract an operator t l h is said to be complex symmetric if there exists a conjugation j on h such that t j t j in this paper we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications in particular we consider the operator matrix of the form t a b 0 j a j where j is a conjugation on h we show that if a is complex symmetric then t is decomposable if and only if a is furthermore we provide some conditions so that a weyl s theorem holds for the operator matrix t

existence and global attractivity of positive periodic solution for an impulsive lasota wazewska model abstract sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive lasota wazewska model for the survival of red blood cells

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

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

asymptotic behaviour of solutions to parabolic elliptic variational inequalities in a real hilbert space h where j is a given interval in r 0 co j is the subdifferential of a convex function 4 on h and b is a maximal monotone operator in h the abstract setting reflects the form of a class of parabolic elliptic boundary value problems with time dependent obstacles such problems arise in particular as mathematical models of various processes in electrochemical technology and some flows with saturations in porous media time dependent obstacles may represent geometric controls moving control actions in these problems in particular such controls may be comprehended in variable boundary conditions prescribed over time dependent parts of the boundary of domain or in source terms distributed over time dependent subdomains the former refers to control of flows via variable water table in reservoirs the latter characterizes control of electrochemical process via mechanically driven motion of a toolpiece cathode the most typical control objective consists there in stabilizing the state of the process at a given spatial distribution for example constant water head and desired shape of anode this motivates our interest in the asymptotic behavior of solutions to the corresponding boundary value problems as t a to the knowledge of the authors this question has so far not been studied in literature as it has been shown in kenmochi pawlow 16 171 the class of considered time dependent problems admits a representation in the form of evolution equation e b in 16 171 the corresponding results on existence uniqueness and stability of solutions have been established in the present paper we study the asymptotic properties of solutions to e c b as t 00 provided some hypotheses are imposed on the family t e r and the limit 4 of as t a for the solution u u of e d b on r we prove that

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

means of unitaries conjugations and the friedrichs operator abstract if c is a conjugation an isometric conjugate linear involution on a separable complex hilbert space h then t b h is called c symmetric if t c t c in this note we prove that each c symmetric contraction t is the mean of two c symmetric unitary operators we discuss several corollaries and an application to the friedrichs operator of a planar domain

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

oscillation and stability of linear impulsive delay differential equations the main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses the results of this paper can be used to improve and derive some of the known results in the literature

stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks in this paper we investigate the stochastic functional differential equations with infinite delay some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using razumikhin method and lyapunov functions based on the obtained results we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays the result extends and improves the earlier publications two examples are given to illustrate the applicability of the obtained results

stability switches and hopf bifurcations of an isolated population model with delay dependent parameters the dynamical behaviors of an isolated population model involving delay dependent parameters are investigated it is shown that the positive equilibrium switches from being stable to unstable and then back to stable as the delay increases and the hopf bifurcation occurs finite times between the two critical values of stability changes which can be analytically determined moreover the bifurcating periodic solutions are expressed analytically in an approximate form by the perturbation approach and floquet technique the direction and stability of the bifurcating periodic solutions are also determined finally the validity of the results is shown by the consistency with the numerical simulations

another note on weyl s theorem weyl s theorem holds for an operator t on a banach space x when the complement in the spectrum of the weyl spectrum coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity this is close to but not quite the same as equality between the weyl spectrum and the browder spectrum which in turn ought to but does not guarantee the spectral mapping theorem for the weyl spectrum of polynomials in t in this note we try to explore these distinctions recall 2 4 6 that a bounded linear operator t e bl x x on a banach space x is fredholm if t x is closed and both t 1 0 and x cl tx are finite dimensional in this case we define the index of t by index t dim t 1 0 dim x t x an operator t e bl x x is called weyl if it is fredholm of index zero and is called browder if it is fredholm of finite ascent and descent equivalently 6 theorem 7 9 3 if t is fredholm and t ai is invertible for sufficiently small a 0 in c the fredholm essential spectrum uess t the weyl spectrum wess t and the browder spectrum wcmm t of t are defined by 0 1 jess t a e c t ai is not fredholm 0 2 wess t a e c t ai is not weyl and 0 3 wecssmm t e c tai is not browder evidently 0 4 jess t c wess t c wcomm t cess t u acc v t where we write acc k for the accumulation points of k c c and av t for the usual spectrum of t if we write iso k k acc k and 0 5 leftr t a e iso 5 t 0 dim tai 1 0 xo for the isolated eigenvalues of finite multiplicity and 6 9 8 3 4 0 6 troo t a5 t wcomm t for the riesz points of t then 6 theorem 9 8 4 with the help of the punctured neighbourhood theorem 0 7 iso v t jess t iso 5 t wess t troo t c 4left t received by the editors december 18 1995 1991 mathematics subject classification primary 47a10

boundedness of the solutions of impulsive differential systems with time varying delay in this paper we investigate boundedness of the solutions of impulsive functional differential equations with time varying delay by using lyapunov functions and razumikhin techniques we will see that impulses do contribute to the solutions boundedness property

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

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

razumikhin type theorems on exponential stability of impulsive infinite delay differential systems in this note we study the exponential stability of impulsive functional differential systems with infinite delays by using the razumikhin technique and lyapunov functions several razumikhin type theorems on exponential stability are obtained which shows that certain impulsive perturbations may make unstable systems exponentially stable some examples are discussed to illustrate our results

sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models by using the theory of coincidence degree the existence of positive periodic solutions is studied for the neutral model with periodic delaysn t n t a t email protected t n t email protected i 1 nb i t n email protected i t email protected i 1 nc i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

periodic solutions of parabolic elliptic obstacle problems this paper deals with parabolic elliptic obstacle problems the problem is formulated as follows let sz be a bounded domain in rn iv 1 and for each i e r let 9 t be a relatively compact domain in sz for a given interval z to tl cc d to t co we then define non cylindrical subsets qjz i 1 2 of ix sz by

an elliptic parabolic free boundary problem in which c is a continuous nondecreas rg function defined on r such that c u is strictly increasing when u 0 ui 1 if bi 0 and bi 1 if ai 0 for i 0 and i 1 and fo fi and t are prescribed functions problem i arises in the theory of fluid aow through pargaily saturated media then t6 denotes the potential due to capiitary suction and c the moisture content the dependence of c on ie is found empirically to be as in fig i c being bounded above by the saturation value c 1 thus in regions where the medium is saturated the flow is of potential type and described by an ehiptic equation and in regions where the medium is unsaturated the flow is of diffusive type and described by a parabolic equation at the boundary between these regions the interface one expects u 0 and u continuous

the euler scheme and its convergence for impulsive delay differential equations this paper presents a fixed stepsize euler scheme for linear impulsive delay differential equations and considers its convergence we propose a method to take the partition nodes for the euler scheme employing the induction and the technique of inequality we obtain the order of convergence for euler scheme an example is given to illustrate the efficiency of our result

input to state stability for discrete time delay systems via the razumikhin technique this paper aims to study the problem of input to state stability iss for discrete time delay systems by employing the razumikhin technique and suitable lyapunov functions backward and forward razumikhin type iss theorems that guarantee the global iss global asymptotic iss and global exponential iss for general discrete time delay systems are established moreover razumikhin type global exponential iss theorems give the estimation of the convergence speed as an application the razumikhin type exponential iss result is used to derive exponential iss criteria for a class of interconnected discrete systems with coupling time delays and disturbance inputs finally examples are given to illustrate the results

on complex symmetric toeplitz operators abstract in this paper we give a characterization of a complex symmetric toeplitz operator t on the hardy space h 2 moreover if t is a complex symmetric toeplitz operator we provide a necessary and sufficient condition for t to be normal finally we investigate these t with finite symbols

exponential stability for impulsive delay differential equations by razumikhin method abstract in this paper we study exponential stability for impulsive delay differential equation of the form x t f t x t t t k x t i k t x t t t k k n by employing the razumikhin technique and lyapunov functions several exponential stability criteria are established some examples are also discussed to illustrate our results

existence theorem for periodic solutions of higher order nonlinear differential equations abstract we study the existence of periodic solutions to differential equations of the form l x g t x x x m f t with l x x m a m 1 x m 1 a 1 x

vector lyapunov functions for practical stability of nonlinear impulsive functional differential equations this paper studies the practical stability of the solutions of nonlinear impulsive functional differential equations the obtained results are based on the method of vector lyapunov functions and on differential inequalities for piecewise continuous functions examples are given to illustrate our results

existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay abstract in this paper we discuss local and global existence and uniqueness results for first order impulsive functional differential equations with multiple delay we shall rely on a nonlinear alternative of leray schauder for the global existence and uniqueness we apply a recent nonlinear alternative of leray schauder type in frechet spaces due to m frigon and a granas resultats de type leray schauder pour des contractions sur des espaces de frechet ann sci math quebec 22 2 1998 161 168 the goal of this paper is to extend the problems considered by a ouahab local and global existence and uniqueness results for impulsive differential equations with multiple delay j math anal appl 323 2006 456 472

existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model abstract by means of the cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population

impulsive periodic boundary value problems of first order differential equations in this paper by using schaeffer s theorem we prove new existence theorems for a nonlinear periodic boundary value problem of first order differential equations with impulses our results improve and generalize some known results

existence and uniqueness of positive periodic solutions for a neutral logarithmic population model in this paper by using an abstract continuous theorem of k set contractive operator the criteria is established for the existence global attractivity of positive periodic solution of a neutral delay logarithmic population model with multiple delays the result improve the known ones in s p lu w g ge existence of positive periodic solutions for neutral logarithmic population model with multiple delays j comput appl math 166 2 2004 371 383

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

existence of positive periodic solution of an impulsive delay logistic model abstract in this paper we use the continuation theory for k set contractions to study the existence of positive periodic solutions of the impulsive delay logistic model x t r t x t 1 x t k t t t k x t k x t k b k x t k k 1 2 the sufficient conditions of the existence of positive periodic solution are obtained

asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations this paper is concerned with stability and asymptotical stability of a class of impulsive delay differential equations iddes stability and asymptotical stability of the system of iddes are studied by the properties of delay differential equations ddes without impulsive perturbations base on this idea numerical methods of iddes are constructed stability and asymptotical stability of numerical methods of iddes are also studied by the properties of numerical methods of ddes